Question

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

Answer 1

y = (x - 2)² - 25

Step-by-step explanation:

The vertex form of a quadratic function is given as:

y = a(x - h)² + k

Where,

(h, k) = vertex = (2, -25)

Now, on substituting the vertex, we get,

y = a(x - 2)² - 25

The above obtained is quadratic function with a vertex.

From question, the point given is (7, 0).

Now, on substituting the point, we get,

0 = a (7 - 2)² - 25

0 = 25a - 25

a = 1

Therefore, the quadratic equation with x-intercept is:

∴ y = (x - 2)² - 25