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anonymous
 one year ago
A sandbag was thrown downward from a building. The function f(t) = 16t2  64t + 80 shows the height f(t), in feet, of the sandbag after t seconds:
Part A: Factor the function f(t) and use the factors to interpret the meaning of the xintercept of the function.
anonymous
 one year ago
A sandbag was thrown downward from a building. The function f(t) = 16t2  64t + 80 shows the height f(t), in feet, of the sandbag after t seconds: Part A: Factor the function f(t) and use the factors to interpret the meaning of the xintercept of the function.

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jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3so... .what did you get for the function factors?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I dont understand what to do

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3well, have you covered quadratic factoring yet? as in factoring quadratic equations, or equations of 2nd degree

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3so... the xintercepts or "zeros" or solutions of the quadratic are when y = 0, or f(x) is 0 so \(\bf f(t)=16t^264t+80\implies 0=16t^264t+80 \\ \quad \\ 16t^2+64t80=0\implies 16(t^2+4t5)=0\) so... any idea on the factors?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im not exactly sure, im not exactly good at this. Can you explain what to do? I dont understand how to factor out 16(t^2+4t5)=0.

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3\(\bf f(t)=16t^264t+80\implies 0=16t^264t+80 \\ \quad \\ 16t^2+64t80=0\implies 16(t^2+4t5)=0 \\ \quad \\ t^2+4t5=\cfrac{0}{16}\implies t^2+4t5=0\) how about now?

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3yeap.... 1 and 5 are the xintercepts

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you help with me part b?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Part B: Complete the square of the expression for f(x) to determine the vertex of the graph f(x). would this be maximum or minimum on the graph?

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3do you know what a perfect square trinomial is?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Isnt the middle number supposed to be 2 times more then ones on the side>?

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3yes site is a bit sluggish :/

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3yeap so... let us do some grouping first \(\bf f(t)=16t^264t+80\implies 16t^2+64t80=f(t) \\ \quad \\ (16t^2+64t)80=f(t)\implies (16t^2+64t+{\color{red}{ \square }}^2)80=f(t)\) any ideas on what our missing number is there, to get a "perfect square trinomial" from the parenthesized group?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.08? OR 10? I dont know. im confused again.

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3well... lemme simplify it some \(\bf f(t)=16t^264t+80\implies 16t^2+64t80=f(t) \\ \quad \\ (16t^2+64t)80=f(t)\implies 16(t^2+4t)80=f(t) \\ \quad \\ 16(t^2+4t+{\color{red}{ \square }}^2)80=f(t)\)

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3hmm actually, should be negative f(t) btw =) so \(\bf f(t)=16t^264t+80\implies 16t^2+64t80=f(t) \\ \quad \\ (16t^2+64t)80=f(t)\implies 16(t^2+4t)80=f(t) \\ \quad \\ 16(t^2+4t+{\color{red}{ \square }}^2)80=f(t)\)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[ax^2+bx+c \\ =ax^2+\frac{a}{a}bx+c \\ \text{ I multiplied the second term by } \frac{a}{a} \\ \text{ I did this because I thought it would be easier } \\ \text{ for you to understand how I factor out } a \\ \text{ from the first two terms in the following step } \\ =a(x^2+\frac{1}{a}bx)+c \\ \\ =a(x^2+\frac{b}{a}x)+c \\ \text{ I'm going to leave a space } \\ \text{ this space will be meant for the number we need to add in } \\ \text{ so that we can complete the square } \\ \text{ but remember whatever I add in } \\ \text{ I have to subtract it out } \] \[=\color{red}{a}(x^2+\frac{b}{a}x+\color{red}{(\frac{b}{2a})^2})+c \color{red}{a(\frac{b}{2a})^2 }\\ =a(x+\frac{b}{2a})^2+ca(\frac{b}{2a})^2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0why is the f(t) negative? and is it 2?

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3ohh, because I moved over to the righthand side =)

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3yes....but, notice, there's a 16 outside the group so, if we expand it, it'd be 16 * 2, or 32 so hold the mayo

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3keep in mind, as freckles said, all we're doing is "borrowing" from our good friend Mr Zero, 0 so if we ADD \(16*2\), we also have to SUBTRACT \(16*2^2\) one sec

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how do you vind the vertex? or the maximum or minimum? Im getting lost

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3\(\bf 16(t^2+4t+{\color{red}{ 2 }}^2{\color{red}{ 2}}^2)80=f(t) \\ \quad \\ 16(t^2+4t+{\color{red}{ 2}}^2)(16\cdot {\color{red}{ 2}}^2)80=f(t) \\ \quad \\ 16(t+2)^26480=f(t) \\ \quad \\ f(t)=16(t+2)^2+64+80 \\ \quad \\ f(t)=16(t+2)^2+144\implies f(t)=16(t{\color{brown}{ (2)}})^2+{\color{blue}{ 144}} \\ \quad \\ \quad \\ y=(x{\color{brown}{ h}})^2+{\color{blue}{ k}}\\ x=(y{\color{blue}{ k}})^2+{\color{brown}{ h}}\qquad\qquad vertex\ ({\color{brown}{ h}},{\color{blue}{ k}})\) see the vertex now?

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3a vertex is where the graph makes a Uturn

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3also, notice, the number in front of the parentheses, is negative, 16 that means, the parabola opens downards, or it is going downdw:1443656451839:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what is the negative 2 for?

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3the xaxis \(\Large \begin{array}{ccccc} (&2&,&144&)\\ &x&&y \end{array} \) http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiItMTZ4XjItNjR4KzgwIiwiY29sb3IiOiIjRTMxMDEwIn0seyJ0eXBlIjoxMDAwLCJ3aW5kb3ciOlsiLTE3LjEzNTU0NDM4OTAyMDYzNyIsIjIyLjUzNzMwNzE3MzQ3OTMwNiIsIjEyMy42MzAzNzA3NzAxMTUyNiIsIjE0OC4wNDQ0MzMyNzAxMTUyIl19XQ

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the highest point is 144? and it would have a maximum not a minimum?

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3is a maximum because the parabola goes up up up up, reaches there, makes a Uturn, then goes back down down down to infinity so the "maximum" point it reaches, is at the vertex, at 2, 144

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Part C: Use your answer from part B to determine the axis symmerty

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Just divide the graph in half right?

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3axis of symmetry ...yes, divide it in halfdw:1443656899492:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So how do describe that? with just a number? or im confused. i know you have to go down the middle but whats after that?

jdoe0001
 one year ago
Best ResponseYou've already chosen the best response.3the axis of symmetry is just a line thus you write the equation of that line in this case is a vertical line, which is \(\bf x= 2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Awe, thank you so much for your help! I have such a better understanding now!
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