MHB Finding the Equation of a Parabola

[missnerdist]

Find the equation of a quadratic function whose graph contains the given points.
(-2,1), (-6,1), (2,-7)

THANK YOU

 

[skeeter]

Find the equation of a quadratic function whose graph contains the given points.
(-2,1), (-6,1), (2,-7)

solve the system for $$y = ax^2+bx+c$$ ...

$a(-2)^2 + b(-2) + c = 1$

$a(-6)^2 + b(-6) + c = 1$

$a(2)^2 + b(2) + c = -7$

 

[skeeter]

One other method ... note the two coordinates with the same y-value.

a parabola's vertical line of symmetry would pass through the midpoint of those two points, i.e. $x=-4$

using the vertex form for a quadratic equation, $y=a(x-h)^2+k$, the vertex is at the coordinates $(h,k)$.

so, you know $h=-4$ and you have three sets of coordinates ... you should be able to substitute those values to determine the constants $a$ and $k$.