# What is the equation of the parabola that has a vertex at  (42, 7)  and passes through point  (37,32) ?

Jan 24, 2016

$y = {\left(x - 42\right)}^{2} + 7$

#### Explanation:

The vertex form of the quadratic function is :

$y = a {\left(x - h\right)}^{2} + k$

where (h , k ) are the coordinates of the vertex .

hence equation can be written as :

$y = a {\left(x - 42\right)}^{2} + 7$

Substitute ( 37 ,32 ) into equation to find a.

ie $a {\left(37 - 42\right)}^{2} + 7 = 32 \Rightarrow 25 a + 7 = 32$

so 25a = 32 - 7 = 25 and a = 1

equation is therefore : $y = {\left(x - 42\right)}^{2} + 7$
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