Question 1181396
Hi can someone help with this question?
the equation of the axis of symmetry is x=-1 the vertex is on the x axis and the parabola passes through the point (1,-4).
<pre>The equation of a parabola with its vertex on the x-axis is one with a vertical axis of symmetry and will be of the form: {{{matrix(1,3, y, "=", a(x - h)^2 + k)}}}.
With its vertex on the x-axis and axis of symmetry being - 1, the parabola's vertex is (h, k) = (- 1, 0).
And, with it passing through point (1, - 4), the vertex-form above, {{{matrix(1,3, y, "=", a(x - h)^2 + k)}}} becomes: 
                                                                  {{{matrix(1,3, - 4, "=", a(1 - - 1)^2 + 0)}}} ------- Substituting (- 1, 0) for (h, k), and (1, - 4) for (x, y)
                                                                 {{{matrix(5,3, - 4, "=", a(1 + 1)^2 + 0, - 4, "=", a(2)^2 + 0, - 4, "=", 4a, (- 4)/4, "=", a, - 1, "=", a)}}}
Substituting - 1, for a, and (- 1, 0) for (h, k) in vertex-form of a parabolic equation, or {{{matrix(1,3, y, "=", a(x - h)^2 + k)}}}, we get:
                                                 Equation of THIS parabola, in vertex-form: {{{highlight_green(matrix(1,3, y, "=", - (x + 1)^2))}}}