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help_people
 one year ago
The height of water shooting from a fountain is modeled by the function f(x) = −4x2 + 24x − 29 where x is the distance from the spout in feet. Complete the square to determine the maximum height of the path of the water.
−4(x − 3)2 − 29; The maximum height of the water is 3 feet.
−4(x − 3)2 − 29; The maximum height of the water is 29 feet.
−4(x − 3)2 + 7; The maximum height of the water is 7 feet.
−4(x − 3)2 + 7; The maximum height of the water is 3 feet.
help_people
 one year ago
The height of water shooting from a fountain is modeled by the function f(x) = −4x2 + 24x − 29 where x is the distance from the spout in feet. Complete the square to determine the maximum height of the path of the water. −4(x − 3)2 − 29; The maximum height of the water is 3 feet. −4(x − 3)2 − 29; The maximum height of the water is 29 feet. −4(x − 3)2 + 7; The maximum height of the water is 7 feet. −4(x − 3)2 + 7; The maximum height of the water is 3 feet.

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help_people
 one year ago
Best ResponseYou've already chosen the best response.0@welshfella or @triciaal or someone :D

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438815884398:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438816139795:dw

help_people
 one year ago
Best ResponseYou've already chosen the best response.0i do not understand any of this i do but what she'll i do next :)

help_people
 one year ago
Best ResponseYou've already chosen the best response.0what is after that part @triciaal

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0one approach compare your equation with the general equation identify your a, b, c and substitute

help_people
 one year ago
Best ResponseYou've already chosen the best response.0how she'll i do that or could you show me I'm confused if you cannot tell

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0alternative dw:1438816378738:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0when you complete the square you are making a perfect square

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438816857649:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0does it make more sense now?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@help_people have you covered what a "perfect square trinomial" is? sometimes just called "perfect square" if not, this may be the time to check your book for it then

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so.. this rings a bell \(\begin{array}{cccccllllll} {\color{brown}{ a}}^2& + &2{\color{brown}{ a}}{\color{blue}{ b}}&+&{\color{blue}{ b}}^2\\ \downarrow && &&\downarrow \\ {\color{brown}{ a}}&& &&{\color{blue}{ b}}\\ &\to &({\color{brown}{ a}} + {\color{blue}{ b}})^2&\leftarrow \end{array}\qquad % perfect square trinomial, negative middle term \begin{array}{cccccllllll} {\color{brown}{ a}}^2&  &2{\color{brown}{ a}}{\color{blue}{ b}}&+&{\color{blue}{ b}}^2\\ \downarrow && &&\downarrow \\ {\color{brown}{ a}}&& &&{\color{blue}{ b}}\\ &\to &({\color{brown}{ a}}  {\color{blue}{ b}})^2&\leftarrow \end{array}\) right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let's see your equation, and let us do some grouping, as triciaal was indicating \(\bf f(x)=4x^2+24x29\implies y=4x^2+24x29 \\ \quad \\ y=(4x^2+24x)29\implies y=4(x^2+6x)29\impliedby \textit{common factor}\) follow that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well... actually we took out 4, should be 6, one sec

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\bf f(x)=4x^2+24x29\implies y=4x^2+24x29 \\ \quad \\ y=(4x^2+24x)29\implies y=4(x^26x)29\impliedby \textit{common factor}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so... follow that so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so \(\bf y=4(x^26x)29\implies y=4(x^26x+{\color{red}{ \square }}^2)29\) so... we have a missing number there, to make a "perfect square trinomial" what do you think that number is anyway?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0notice \(\begin{array}{cccccllllll} {\color{brown}{ a}}^2& + &2{\color{brown}{ a}}{\color{blue}{ b}}&+&{\color{blue}{ b}}^2\\ \downarrow && &&\downarrow \\ {\color{brown}{ a}}&& &&{\color{blue}{ b}}\\ &\to &({\color{brown}{ a}} + {\color{blue}{ b}})^2&\leftarrow \end{array}\qquad % perfect square trinomial, negative middle term \begin{array}{cccccllllll} {\color{brown}{ a}}^2&  &2{\color{brown}{ a}}{\color{blue}{ b}}&+&{\color{blue}{ b}}^2\\ \downarrow && &&\downarrow \\ {\color{brown}{ a}}&& &&{\color{blue}{ b}}\\ &\to &({\color{brown}{ a}}  {\color{blue}{ b}})^2&\leftarrow \end{array}\) the middle term is just the other two terms without the "2" exponent times 2 and our last number is hidden in the middle term

help_people
 one year ago
Best ResponseYou've already chosen the best response.0or 3 i meant to say @jdoe0001

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right.... 2 * x * 3 = 6x < middle term

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0bear in mind two things one there's a 4 outside the group, that is multiplying the group and that what we're really doing is borrowing from our good fellow Mr Zero, 0 so, if we add anything, we also have to subtract it so, we'll add \(3^2\) but is being multiplied by the 4 outside, that means that we're really adding \(3^2 \)cdot 4 = 36

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and if we're adding 36, well, really subtracting, since it's negative we also have to add it so that 36 + 36 = 0 and our good felow Mr Zero gets back his figure

help_people
 one year ago
Best ResponseYou've already chosen the best response.0wait so the final answer is a ? @jdoe0001

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ahemm nope.. one sec

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\bf y=4(x^26x)29\implies y=4(x^26x+{\color{red}{ 3 }}^2)+3629 \\ \quad \\ y=4(x3)^27 \\ \quad \\ \quad \\ y=(x{\color{brown}{ h}})^2+{\color{blue}{ k}} \qquad\qquad vertex\ ({\color{brown}{ h}},{\color{blue}{ k}})\) so... what do you think is the vertex? or that ycoordinate for that matter

help_people
 one year ago
Best ResponseYou've already chosen the best response.0its either a or b 2 @jdoe0001

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\bf yy=4(x^26x)29\implies y=4(x^26x+{\color{red}{ 3 }}^2)+3629 \\ \quad \\ y=4(x{\color{brown}{ 3}})^2+{\color{blue}{ 7}} \\ \quad \\ \quad \\ y=(x{\color{brown}{ h}})^2+{\color{blue}{ k}} \qquad\qquad vertex\ ({\color{brown}{ h}},{\color{blue}{ k}}) \) can you see the vertex now?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0shoot even got 2 yy, =( \(\bf y=4(x^26x)29\implies y=4(x^26x+{\color{red}{ 3 }}^2)+3629 \\ \quad \\ y=4(x{\color{brown}{ 3}})^2+{\color{blue}{ 7}} \\ \quad \\ \quad \\ y=(x{\color{brown}{ h}})^2+{\color{blue}{ k}} \qquad\qquad vertex\ ({\color{brown}{ h}},{\color{blue}{ k}}) \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0see the vertex now? see the ycoordinate? the ycoordinate of the verex, is the "maximum height" because the vertex is the Uturn point for the graph, it goes up, reaches a maximum, then back down

help_people
 one year ago
Best ResponseYou've already chosen the best response.0ok so i am trying to find the answer lol is it a or b i said it was a but you said i was wrong @jdoe0001

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well.... thata form of the quadratic is the socalled "vertex form" because it shows the vertex coordinates "x" is the horizontal distance "y" is the vertical height the equation has a leading term negative coefficient, thus is opening downwards thus the maximum point for it, is at the vertex

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and is obtained by "completing the square" so... the vertex should be pretty obvious there and so is the ycoordinate of the vertex and that ycoordinate, is the maximum height of it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dunno... what do you think is the vertex? notice to the equation in vertex form

help_people
 one year ago
Best ResponseYou've already chosen the best response.0vertex is 3 and 7 @jdoe0001

help_people
 one year ago
Best ResponseYou've already chosen the best response.0based on that i bleive its a @jdoe0001

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438820047108:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0equaiont in "a" doesn't even look like the obtained equation so it can't be that

help_people
 one year ago
Best ResponseYou've already chosen the best response.0the only other one i would think is c @jdoe0001

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\(\bf 4(x  {\color{brown}{ 3}})^2 {\color{blue}{ 29 }}\) according to that, the vertex is 3, 29 which is not what the simplified version is

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeap, the maximum height of the water is 7 units vertex at 3,7dw:1438820313064:dw

help_people
 one year ago
Best ResponseYou've already chosen the best response.0@triciaal please come back he just left and i am not sure what the answer is :/

help_people
 one year ago
Best ResponseYou've already chosen the best response.0i first thought it was a but then he told me no so now i believe it is c
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