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- anonymous

Two quadratic functions are shown.
Function 1:
f(x) = 2x2 − 8x + 1 Function 2:
x g(x)
−2 2
−1 −3
0 2
1 17
Which function has the least minimum value and what are its coordinates?
Function 1 has the least minimum value and its coordinates are (0, 1).
Function 1 has the least minimum value and its coordinates are (2, −7).
Function 2 has the least minimum value and its coordinates are (0, 2).
Function 2 has the least minimum value and its coordinates are (−1, −3).
WILL FAN AND MEDAL

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- anonymous

- katieb

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- anonymous

I'm really more of a visual learner, so what I would do is graph the points given and the equation of the graph and calculate the vertex coordinates afterwards, however, you will not always be given that option in standardized testing.
What do you think the correct answer is?

- anonymous

Recall that the vertex formula is:
x = -b/2a
(Then plug in value for all values of x to obtain value y)

- anonymous

I think the correct answer might be either A or B. I feel like im doing it wrong

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- campbell_st

for the 1st equation, find the line of symmetry, the minimum value is on that line
it is also the x value on the vertex...
\[x = \frac{-b}{2a}\]
you have b = -8 and a = 2
so find x,
then substitute it into the original equation to find the minimum value
hope it helps

- campbell_st

for the 2nd function, the minimum value is the smallest y value... so looking at the te table the minimum value is y = -3 so the vertex is (0, -3)
then compare this to the answer in the 1st part

- anonymous

@Aureyliant was i right??

- anonymous

Try following the steps @campbell_st provided :)

- anonymous

@campbell_st how do i find x for the first one

- campbell_st

ok.... the general from of the quadratic is
\[ax^2 + bx + c\]
comparing this you your equation you have
b = -8 and a = 2
does that make sense..?

- anonymous

so would it be c?

- campbell_st

no... ignore the choices for the minute
so to find x
\[x = \frac{-(-8)}{2 \times 2}\]
what is the value for x..?

- anonymous

- campbell_st

great so now substitute it into the equation, this will give the minimum value
\[f(2) = 2\times(2)^2 - 8 \times 2 + 1\]
what is the value of f(2)

- anonymous

-7?

- campbell_st

great so the vertex of function 1 is at (2, -7)
function 2, reading the table has a minimum value at (1, -3)
so which function is further down the y-axis..?

- anonymous

function 2

- campbell_st

you need to compare the y values.... y = -7 and y = -3

- campbell_st

|dw:1434572812211:dw|

- campbell_st

its not function 2

- campbell_st

and the use the vertex in function 1 as part of the answer

- anonymous

thank you!

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