# What is the equation of the parabola that has a vertex at # (7, 3) # and passes through point # (3, -2) #?

##### 1 Answer

Feb 12, 2017

#### Explanation:

Standard form of a quadratic function

There are 3 unknowns a, b and c. We need 3 equations.

a. x-coordinate of vertex = 7

b. y-coordinate of vertex = 3

y vertex = f(7) = 3 --> 3 = 49a + 7b + c (2)

c. The parabola passes at point (3, -2)

f(3) = -2 = 9a + 3b + c (3)

Now, solve the system of 3 equations (1), (2) and (3) to get a, b, and c

Equation (2) --> 3 = 49a + 7b + c = 49a - 98a + c = - 49a + c (2)'

Equation (3) --> - 2 = 9a + 3b + c = 9a - 42a + c = - 33a + c (3)'

Subtract (3)' from (2)', we get: - 33a = 5 -->

c = -3