Question

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

Answer 1

The equation of the quadratic function is y = (x - 2)² - 25

How to determine the equation of the quadratic function

From the question, we have the following parameters that can be used in our computation:

Vertex = (2, -25)

x-intercept = (7,0)

The equation of the quadratic function is represeted as

y = a(x - h)² + k

Using the vertex, we have

y = a(x - 2)² - 25

Using the other point, we have

a(7 - 2)² - 25 = 0

25a =25

a = 1

Recall that

y = a(x - 2)² - 25

So, we have

y = (x - 2)² - 25

Hence, the equation of the quadratic function is y = (x - 2)² - 25

Answer 2

y = (x − 2)² − 25

Explanation:

Vertex form of a quadratic is:

y = a (x − h)² + k

where (h, k) is the vertex.

Given that h = 2 and k = -25:

y = a (x − 2)² − 25

And given that a point is (7, 0):

0 = a (7 − 2)² − 25

0 = 25a − 25

a = 1

Therefore, the equation is:

y = (x − 2)² − 25