Write the equation of the parabola that has the vertex at point (5,0) and passes through the point (7,−2).

Question

So please tell the equation!!!

Answer 1

The Vertex form of a parabola (quadratic equation) is y = a (x-h)^2 + k, where h and k are the coordinates of the vertex given as (5,0). Plug in (5,0) into the general equation, y = a (x-5)^2 + 0  or y = a (x-5)^2. "a" is the leading coefficient for all forms of a quadratic equation: standard form, vertex form and intercept form.

In this problem, you are given a point on the parabola so you can solve for "a". Plug in the point coordinates (7, -2) into y = a (x-5)^2 to solve for "a",  -2 = a (7-5)^2 or a= -1/2.

 

The final equation for the parabola described in the problem statement is therefore, y = -1/2 (x-5)^2

Answer 2

y = a(x-h)² + k

-2 = a(7-5)² + 0

-2 = 4a

-1/2 = a

y = (-1/2)(x-5)²