Question

roots -2 and 4 and vertex 1,-10

Answer 1

Is this a parabola?

Answer 2

quadratic function

Answer 3

Ah, same thing.

The general form of a quadratic function is \(y=ax^2+bx+c\). You're given that the roots are \(-2\) and \(4\), which means \(y=0\) when \(x=-2,4\).

So you have the following
\[0=a(-2)^2+b(-2)+c\\
0=a(4)^2+b(4)+c\]
\[\begin{cases}4a-2b+c=0\\16a+4b+c=0\end{cases}\]
You're also given another point, \((1,-10)\), which means \(y=-10\) when \(x=1\). Plugging in this \(x\), you get
\[-10=a(1)^2+b(1)+c\\
a+b+c=-10\]
So, in sum, you have the following system of three equations with three unknowns:
\[\begin{cases}4a-2b+c=0\\16a+4b+c=0\\a+b+c=-10 \end{cases}\]
Your task now is to solve for \(a,b,c\).