The graph of y = ax 2 + bx + c is a parabola that opens up and has a vertex at (-2, 5). what is the solution set of the related equation 0 = ax 2 + bx + c?

I have provided two solutions both concluding the same thing.

There is no solution.

Simplest solution says this is a parabola opened up at vertex (-2,5) which means it never crosses the x-axis.  There is no solution because thee curve does not touch the x-axis.

Step-by-step explanation:

Harder solution (algebraic solution):

The vertex form a parabola is

We are given the vertex (h,k) is (-2,5)

So we have

Now we also know since the parabola opens up.

That is all we know about a.

Let's see what is in standard form

So we are asked to solve for the solution set of

Plug into quadratic formula

I'm going to write the quadratic formula with the capital letters to be less confusing:

This says has to be negative... The inside of the square root... So there was no real solution.\\

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Simpler solution (graph/visual)

You could have also drawn a parabola open up with vertex at (-2,5) and we should have seen that it was impossible it cross the x-axis.

step-by-step explanation:

if you meant, "on the way from (3, 2) to (3, 14):

x does not change; y increases by 12.

ensure that you have copied down this problem correctly.   .