Answer to Question #130322 in Algebra for Everlyn

Question

Use the graph to determine a. the​ function's domain; b. the​ function's range; c. the​ x-intercepts, if​ any; d. the​ y-intercept, if​ any; and e. the missing function​ values, indicated by question​ marks, below. f(-2)=? f(2)?

A coordinate system has a horizontal x-axis labeled from negative 5 to 5 in increments of 1 and a vertical y-axis labeled from negative 5 to 5 in increments of 1. A parabola that opens upward has vertex (negative 2, negative 1) and passes through the points (negative 4, 0), (0, 0), and left parenthesis 2 comma 3 right parenthesis.

a. The domain is
b. The range is
c. Select the correct choice below and fill in any answer boxes within your choice.
A.The​ x-intercept(s) is​ (are)
d. Select the correct choice below and fill in any answer boxes within your choice.
A.The​ y-intercept is
f(-2)=
f(2)=

Answer 1

a. The curve is parabola with the formula y=ax²+bx+c , so x can be any number and graph domain is $(-\infty, +\infty)$ .

b. As you can see from the graph, y changes from $+\infty$ to -1 in the point (-2,-1) and then again to +$\infty$. So range is $[-1, +\infty).$

c. Points B(-4, 0) and C(0, 0) are points with x-intercepts. In these points y=0.

d. Point C(0, 0) is y-intercept. In this point x=0.

f(-2)=-1 because of coordinates of point A

f(2)=3 because of coordinates of point D