Question 946705

Write the standard form of the equation of the parabola that has the indicated vertex and passes through the given point. Vertex:(4, -1); point:(2,7)
<pre>Vertex form of the equation of a parabola: {{{y = a(x - h)^2 + k}}}
{{{7 = a(2 - 4)^2 + - 1}}} ------ Substituting (4, - 1) for (h, k), and (2, 7) for (x, y)
7 = a(4) - 1
7 + 1 = 4a
8 = 4a
a = {{{8/4}}}, or 2
Vertex form of the equation of this parabola: {{{y = 2(x - 4)^2 - 1}}}
{{{y = 2(x^2 - 8x + 16) - 1}}}
{{{y = 2x^2 - 16x + 32 - 1}}}
Standard form of the equation of this parabola: {{{highlight_green(y = 2x^2 - 16x + 31)}}}