Analyze the key features of the graphs of the functions below. Select all of the quadratic functions that open down, have a vertex that is a maximum and a positive y-intercept. The Choices are F(x)=2x^2-4x-3G(x)= -x^2+x+1H(x)= -2x^2+3x-1M(x)=x^2-9N(x)= -3x^2+7
Accepted Solution
A:
Hello there!
The only thing you need to do is look at the leading coefficient for each choice to decide which ones open down and have a maximum. If the leading coefficient is negative, then they open down and have a maximum.
F(x) is out of our choices because the leading coefficient is positive.
G(x) and H(x) are still options.
M(x) is gone for the same reason we won't choose F(x).
N(x) is still an option.
Now our choices are between G(x), H(x), and H(x). To decide which ones have a positive y-intercept, look at the constant term. If it's negative, then it has a negative y-intercept and it's out of our choices.
G(x) and H(x) remain our only options and since the question can have multiple answers, G(x) and H(x) are the answers!