What is the equation of the parabola that has a vertex at $(0, 0)$ $(0, 0)$ and passes through point $(- 1, - 64)$ $(-1,-64)$ ?

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Answer 1 · 2018-04-20T11:52:07

$f (x) = - 64 x^{2}$ $f(x)=-64x^2$

If the vertex is at (0|0),
$f (x) = a x^{2}$ $f(x)=ax^2$
Now, we just sub in the point $(- 1, - 64)$ $(-1,-64)$

$- 64 = a \cdot {(- 1)}^{2} = a$ $-64=a*(-1)^2=a$
$a = - 64$ $a=-64$
$f (x) = - 64 x^{2}$ $f(x)=-64x^2$

What is the equation of the parabola that has a vertex at (0, 0) (0,0) (0, 0) and passes through point (-1,-64) (−1,−64) (-1,-64) ?