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

User Mikebloch
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The vertex form of the equation of a parabola is

f(x) = a( x − h)^2 + k

where (h,k) is the vertex of the parabola. In this case, we are given that (h,k) = (5,0). Hence,

f(x) = a( x − 5)^2 + 0

=a( x − 5)^2

Since we also know the parabola passes through the point (7,−2), we can solve for a because we know that f(7) = −2.

a( 7 − 5)^2 = -2

a(2)^2 = -2

4a = -2

a = -1/2

Thus, the given parabola has equation

f(x) = -1/2(x − 5)^2

User Tughi
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