Question 1184796
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One form of the general vertex form of the the equation of a parabola is<br>
{{{y-k=a(x-h)^2}}}<br>
The vertex is given as (-2,3), so an equation of the parabola is<br>
{{{y-3=a(x+2)^2}}}<br>
The solution from the other tutor uses the other point (-1,5) and formal algebra to determine the coefficient a; that is of course fine.<br>
Once you become familiar with quadratic equations you can find the coefficient a informally, as follows:<br>
The vertex is (-2,3) and the other given point is (-1,5).  So 1 unit away from the vertex in the x direction the y value has increased by 2.  That means the coefficient a is 2.  So<br>
ANSWER: {{{y-3=2(x+2)^2}}}<br>