What is the equation of the quadratic function with a vertex at (2,-25) and an x-intercept at(7,0)

Question

asked Mar 12, 2021 20.4k views

2 Answers

Scriddie · Answer 1 · 2021-03-18T23:19:10+0000

The equation of the quadratic function is
y=(x-7)(x+3)

Step-by-step explanation:

The vertex form of the quadratic function is given by

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

It is given that the quadratic function has a vertex at
(2,-25)

The vertex is represented by the coordinate
(h,k)

Hence, substituting
(h,k)=(2,-25) in the vertex form, we get,

y=a(x-2)^(2)-25

Now, substituting the x - intercept
(7,0) , we have,

0=a(7-2)^(2)-25

0=a(5)^(2)-25

25=a(25)

1=a

Thus, the value of a is 1.

Hence, substituting
a=1 ,
(h,k)=(2,-25) in the vertex form
y=a(x-h)^(2)+k , we get,

y=1(x-2)^(2)-25

y=(x-2)^(2)-25

y=x^2-2x+4-25

y=x^2-2x-21

y=(x-7)(x+3)

Thus, the equation of the quadratic function is
y=(x-7)(x+3)