Question 887457

Hi there. I need help with these questions. Writing each first in vertex form, and then in standard form.

1) vertex (3,5) and passing through (1,1)
2) vertex (1,-7) and passing through (-2,29)
3) vertex (-6,-5) and passing through (-3,4) 
<pre>
Doing 1 of the 3 should be enough for you to follow
Vertex, or (h, k) = (3, 5), and pass-through point, (x, y) being (1, 1)
Vertex equation-form of a parabola: {{{y = a(x - h)^2 + k}}} becomes:
{{{1 = a(1 - 3)^2 + 5}}} ----- Substituting variables to determine the value of "a"
{{{1 = a(- 2)^2 + 5}}}
1 = 4a + 5
4a = 1 - 5
4a = - 4
{{{a = (- 4)/4}}}, or - 1

Vertex form:   {{{highlight_green(highlight_green(y = - (x - 3)^2 + 5))}}}
{{{y = - (x - 3)^2 + 5}}}
{{{y = - (x^2 - 6x + 9) + 5}}}
{{{y = - x^2 + 6x - 9 + 5}}}
Standard form: {{{highlight_green(highlight_green(y = - x^2 + 6x - 4))}}}