Question

the vertex of a quadratic function is (6, 2), and the y-intercept of the function is (0, −70). the equation of the function in vertex form, f(x) = a(x - h)2 k, is shown. –70 = a(0 – 6)2 2 what is the value of a?

Answer 1

Hello,
++++++++++++++++
f(x)=a(x-6)²+2
f(0)=-70==>a(-6)²+2=-70===>36a=-72==>a=-2
++++++++++++++++++++

Answer 2

Answer-

The value of a is -2

Solution-

The vertex form of parabola-

$y=a(x-h)^2+k$

Where, vertex is at (h, k)

Given that the vertex is at (6, 2), so equation would be

$y=a(x-6)^2+2$

As the y intercept is the point which lies on the parabola, so it must satisfy the parabola equation.

$\Rightarrow -70=a(0-6)^2+2$

$\Rightarrow -70-2=a(-6)^2$

$\Rightarrow a(6)^2=-72$

$\Rightarrow 36a=-72$

$\Rightarrow a=-2$