Question 1163354
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With vertex (1,-13), the vertex form of the equation is<br>
{{{(y+13) = a(x-1)^2}}}<br>
Use the given point (0,-11) to determine the coefficient a:<br>
{{{-11+13 = a(-1)^2}}}
{{{2 = a}}}<br>
The equation in vertex form is<br>
{{{(y+13) = 2(x-1)^2}}}<br>
To find the x-intercepts, set y=0 and solve<br>
{{{13 = 2(x-1)^2}}}
{{{(x-1)^2 = 13/2}}}
{{{x = 1+-sqrt(13/2)}}}<br>
You can write those roots in the requested form....<br>
A graph, to let you see if your answers are reasonable....<br>
{{{graph(400,400,-5,5,-15,5,2(x-1)^2-13)}}}<br>