Question 1127572
<br>
Answer the question using the symmetry of the parabola and the vertex form of the equation of a parabola,<br>
{{{y-k = a(x-h)^2}}} where (h,k) is the vertex.<br>
(1) With x-intercepts 3 and 9, the axis of symmetry is x=6, so the equation is of the form<br>
{{{y = a(x-6)^2+k}}}<br>
(2) Use one of the x-intercepts and the third point in that equation to find the value of a:<br><pre>
    (9,0)   -->   0 = a(3^2)+k   9a+k =  0
    (10,-7) -->  -7 = a(4^2)+k  16a+k = -7
                             -----------
                                 7a   = -7
                                    a = -1</pre><br>
The equation is now of the form<br>
{{{y = -1(x-6)^2+k}}}<br>
(3) Use either x-intercept to find k:<br>
{{{0 = -1(9)+k}}}
{{{k = 9}}}<br>
We are done....<br>
ANSWER: {{{y = -1(x-6)^2+9}}}