Question

Identify the quadratic function from the choices below whose parabola opens downward.
A. y = -5x + x2
B. y = 2x2 – 4x
C. y = x2 – 11x + 7
D. y = x – 2x2 + 9

Does the function f(x) = x2 - 2x + 2 have a maximum or minimum value?

A. Maximum
B. Minimum

Answer 1

When a parabola opens downward, that means the equation is negative. If the equation is positive then the parabola will open upward. So which one of the equations is negative?

Answer 2

the negative equation would be y = 2x2 – 4x @CloverRacer right ?

Answer 3

Not quite, that equation is positive. Notice in the graph below the parabola opens upward.

Answer 4

i redid it again and i got something diffrent i'm leanig towards A or D @CloverRacer

Answer 5

Please stop a moment and consider what coefficient / value in a quadratic expression such as the one you've posted tells you whether the curve opens upward or opens downward.

Answer 6

@mathmale Who are you referring to?

Answer 7

Good Job @Ambbiiee ! You are on the right track! (:

Answer 8

since the x is positive the first one has to be D @CloverRacer

Answer 9

@Ambbiiee : Both my questions were directed at you.
How do you determine whether the graph of a given quadratic equation opens up or down?
I don't agree with your statement, "since the x is positive the first one has to be D." What if "x" shows up more than once in the given quadratic?

Answer 10

This is the equation for D, the parabola points downward so the equation is negative.

Answer 11

then its going to be negative @mathmale

Answer 12

It's not whether the "equation" is negative, but rather whether the first term (the term involving x^2) is positive or negative. I'm glad we can discuss this. I urge you not to use pronouns as in "it's going to be positive." Instead, please type the actual name: for example: "Since the x^2 term is positive, the graph opens up."