Question 1155562
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With the vertex on the y-axis at (0,5), the equation is of the form<br>
{{{y = ax^2+5}}}<br>
To find the coefficient a and thus find the equation, plug in the coordinates of the other given point.<br>
{{{-2 = a(1^2)+5}}}
{{{-2 = a+5}}}
{{{a = -7}}}<br>
The equation is {{{y = -7x^2+5}}}<br>
There is another less formal method for finding the coefficient a which you can use if you understand parabolas and quadratic functions.  The equation<br>
{{{y = ax^2+5}}}<br>
tells you that the displacement in y is a times the displacement in x.  From (0,5) to (1,-2) the displacement in x is 1; the square of that is 1.  And the corresponding displacement in y is -7; -7 is -7 times 1, so a is -7.<br>