Question

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

Answer 1

Answer:

The graph in the attached figure

Step-by-step 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