# Determine the equation of the quadrac function with vertex (2,4)

Determine the equation of the quadrac function with vertex (2,4) and passing through the point (-1, -14).
Your answer should be in vertex form.
$f\left(x\right)=$
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Coon2000

Let the vertex form of quadratic function
be
$f\left(x\right)=a{\left(x-h\right)}^{4}+k$, whese (h,k) is
the vertex.
We are given: vertex is (2, 4)
$\therefore n=2,k=4$
$\therefore f\left(x\right)=a{\left(x-2\right)}^{2}+4$
We are aslo given that function
$\left(-1,-14\right)$
we get
$-14=a{\left(-1-2\right)}^{2}+4$
$-14=9a+4$
$-14-4=9⇒9a=-18$
$a=-2$
$\therefore f\left(x\right)=-2{\left(x-2\right)}^{2}+4$