Question

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

Answer 1

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?

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

@Aureyliant was i right??

Answer 7

Try following the steps @campbell_st provided :)

Answer 8

@campbell_st how do i find x for the first one

Answer 9

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..?

Answer 10

so would it be c?

Answer 11

no... ignore the choices for the minute

so to find x

\[x = \frac{-(-8)}{2 \times 2}\]

what is the value for x..?

Answer 12

2 @campbell_st

Answer 13

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)

Answer 14

-7?

Answer 15

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..?

Answer 16

function 2

Answer 17

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

Answer 18

its not function 2

Answer 19

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

Answer 20

thank you!