Question 1202229
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Given the vertex (5,2), the equation in vertex form is of the form<br>
{{{y=a(x-5)^2+2}}}<br>
You can use either of the given x-intercepts to determine the value of the constant a.<br>
{{{0=a(7-5)^2+2}}}
{{{0=4a+2}}}
{{{4a=-2}}}
{{{a=-1/2}}}<br>
ANSWER: {{{y=(-1/2)(x-5)^2+2}}}<br>
When you get familiar with the equations of parabolas, you can determine the constant a without using formal algebra.  In this example, the reasoning would go like this:<br>
From the vertex to either x-intercept, the change in x is 2.  If the function were simply y=x^2, then the corresponding change in y would be 2^2=4.  But the corresponding change in y in this example is -2; and that means the constant a is -2/4 = -1/2.<br>