Question

Given the graph and the equation y = 2x2 - 8x + 3, which one has the smaller minimum and by how much?

A) The graph by 6 units
B) The graph by 70 units
C) The equation by 2 units
D) The equation by 5 units

Answer 1

In f(x) = ax^2 + bx + c, the minimum or the maximum occurs at x = -b/2a.
And the minimum value is f(-b/2a).
Find the minimum of f(x) = 2x^2 - 8x + 3 first.
Then read the minimum value of y from the graph.
Do the comparison.

Answer 2

I'm sorry i dont understand of what you explained

Answer 3

The standard form of a parabola is y = ax^2 + bx + c.
For this parabola, the minimum/maximum occurs at x = -b/2a
compare the standard form of parabola to y = 2x^2 - 8x + 3
What is a, b, c? What is -b/2a?

Answer 4

y = ax^2 + bx + c
y = 2x^2 - 8x + 3
Compare the above two. What is a, b and c?

Answer 5

a=2
b=-8
c=3

Answer 6

Yes. The minimum occurs at x = -b/2a.
Plug in the numbers for a and b and find at what x value the curve will have a minimum.

Answer 7

i got -2 for x

Answer 8

check the sign.

Answer 9

Oh my bad, x=2

Answer 10

Yes, the minimum occurs at x = 2. What is the minimum value?
Just plug x = 2 in y = 2x^2 - 8x + 3 and find the y value.

Answer 11

I got 5 so is the answer d?

Answer 12

check the sign again.

Answer 13

i meant -5. sorry

Answer 14

Equation has a minimum value of -5
Graph has a minimum value of ?

Answer 15

Just read the graph. What is the lowest y-value?

Answer 16

the lowest y-value got it . . . oh so its c.

Answer 17

Yes.

Answer 18

thank you for putting up with me. i suck at graphs. Thanks for helping me! :)

Answer 19

You are welcome. You did well. Just watch out for the +/- signs.

Answer 20

I'll keep that in mind. Thanks