Question

A parabola has an x-intercept of -1, a y-intercept of -3, and a minimum of -4 at x = 1.

Which graph matches this description?

Answer 1

The graph in the attached figure

Explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

`y=a(x-h)^(2)+k`

where

a is a coefficient

(h,k) is the vertex

In this problem we have

(h,k)=(1,-4)

substitute

`y=a(x-1)^(2)-4`

we have

An x-intercept of (-1,0)

substitute and solve for a

`0=a(-1-1)^(2)-4`

`0=4a-4`

`4a=4`

`a=1`

The equation is

`y=(x-1)^(2)-4`

Verify the y-intercept

For x=0

`y=(0-1)^(2)-4`

`y=-3`

The y-intercept is the point (0,-3) -----> is correct

using a graphing tool

see the attached figure