Question 1148201
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Start with the vertex form of the equation, as tutor @MathTherapy did:<br>
{{{y = a(x-h)^2+k}}}<br>
With the vertex given as (4,-3), the equation in this form is<br>
{{{y = a(x-4)^2-3}}}<br>
Then here is an alternative method for determining the value of a to complete the equation.<br>
(1) The point other than the vertex that is given is 2 units to the right of the vertex.
(2) If a were 1, so that the graph behaved like y=x^2, then the y value 2 to the right of the vertex would be 2^2=4 greater than the y value at the vertex.
(3) But the y value 2 to the right of the vertex is only 2 greater than the y value at the vertex.<br>
Since the y value increased only half as much as it would have increased if a were 1, a must be 1/2.<br>
So the equation is<br>
{{{y = (1/2)(x-4)^2-3}}}<br>