# What is the equation of the parabola that has a vertex at # (10, 8) # and passes through point # (5,58) #?

##### 1 Answer

Nov 24, 2015

Find the equation of a parabola.

Ans:

#### Explanation:

General equation of the parabola:

There are 3 unknowns: a, b, and c. We need 3 equations to find them.

x-coordinate of vertex (10, 8):

y-coordinate of vertex:

Parabola passes through point (5, 58)

y(5) = 25a + 5b + c = 58 (3).

Take (2) - (3) :

75a + 5b = -58. Next, replace b by (-20a) (1)

75a - 100a = -50

-25a = -50 -->

From (3) --> 50 - 200 + c = 58 -->

Equation of the parabola: