Question

Two quadratic functions are shown.

Function 1:
f(x) = 2x^2 − 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?
A)Function 1 has the least minimum value and its coordinates are (0, 1).
B)Function 1 has the least minimum value and its coordinates are (2, −7).
C)Function 2 has the least minimum value and its coordinates are (0, 2).
D)Function 2 has the least minimum value and its coordinates are (−1, −3).

Answer 1

@campbell_st

Answer 2

is this calculus of algebra..?

Answer 3

YES IS ALGEBRA

Answer 4

ok... find the line of symmetry for function 1, the formula is

\[x = \frac{-b}{2\times a}\]

the function has a = 2 and b = -8

so can you just calculate that to start

Answer 5

2*-8=?

Answer 6

well not quite

\[x = \frac{-(-8)}{4} = 2\]

so knowing the line of symmetry, you should know that this is the value of x that gives the minimum value...

so substitute x = 2 into function 1 and get a value

Answer 7

so, i need to solve that problem? to star?

Answer 8

no in function 1, just replace x with the number 2 and calculate the value..

Answer 9

\[y = 2 \times 2^2 - 8 \times 2 + 1\]

Answer 10

-7?

Answer 11

great so the mimimum for function 1 is at the point (2, -7)

now look at the table for function 2... what is the minimum y value...?

Answer 12

can you give the problem and i can solve

Answer 13

no, look at the table for function 2, go down the y values and which is the minimum of smallest

Answer 14

3?

Answer 15

im not good at math :/

Answer 16

the y values in the table are 2, -3, 2, 17

which is the smallest..?

Answer 17

oh wait let me solve

Answer 18

its 7?

Answer 19

these are the y values for function 2


y = 2, y = -3, y = 2 and y = 17

which one is the lowest..?

Answer 20

-3?

Answer 21

great so in function 2, the minimum is at the point (-1, -3) y = -3

and remember function 1 has a minimum at (2, -7) y = -7

so compare the y values and decide which is lower...?

Answer 22

the answer its B? IM right?

Answer 23

that's correct

Answer 24

thank you so much!