Question

Compare the graphs of the function, ????(x) = −2(x + 3)^2 + 2 and ????(x) = 5(x + 3)^2 + 2. What do the graphs have

Answer 1

Answer:

Similarity: Both functions has same vertex at point $(-3,2)$.

Difference: $f(x)=-2(x+3)^2+2$ is downward opening parabola, while  $g(x)=5(x+3)^2+2$ is an upward opening parabola.

Step-by-step explanation:

We have been given two functions as: $f(x)=-2(x+3)^2+2$ and $g(x)=5(x+3)^2+2$. We are asked to compare the graphs of the given function.

We know that standard form of a parabola with vertex at point (h,k) is in format $y=a(x-h)^2+k$.

Let us find the similarity in both graphs.

• Upon comparing both functions with standard form of a parabola, we can see that vertex of the both parabolas is at point $(-3,2)$.

Let us find the difference in both graphs.

We can see that leading coefficient of $g(x)=5(x+3)^2+2$ is positive, so it will be an upward opening parabola.

We can also see that leading coefficient of $f(x)=-2(x+3)^2+2$ is negative, so it will be a downward opening parabola.