Question 1184796: Find the equation of the quadratic curve with a turning point at (-2,3) and which passes through (-1,5) Found 2 solutions by MathLover1, greenestamps:Answer by MathLover1(20850) (Show Source):
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Find the equation of the quadratic curve with
if a turning point at (,), that is a vertex: and
so use equation in vertex form
and since passes through (,), use it to calculate
your equation is:
One form of the general vertex form of the the equation of a parabola is
The vertex is given as (-2,3), so an equation of the parabola is
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.
Once you become familiar with quadratic equations you can find the coefficient a informally, as follows:
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
