Standard Form help!

[Giulie]

Here is the math problem in question:

1) Re-write in standard form and sketch the graph to identify the vertex and all intercepts for f(x)=2x[sup:4xp1bnvb]2[/sup:4xp1bnvb]-16x+31.

 

[galactus]

The vertex of a parabola can be easily found from $\displaystyle x=\frac{-b}{2a}$. Then, to find the corresponding y coordinate, plug that x value back into the equation.

To write in standard form, complete the square and get it into the form $\displaystyle a(x-h)^{2}+k$

h and k are the coordinates of the vertex. Check them against the formula I gave at the top.

 

[Giulie]

Thank you so much. The way my tutor helped me do it was so confusing. This helped much more. so f(x)=2(x-4)[sup:24csmgaq]2[/sup:24csmgaq]-1, y-intercept is (0,31) & x-intercept is (4+-square root of 2/2, 0), vertex is (4, -1).