SOLUTION: The vertex of this parabola is at (1, 2). When the x-value is 0, the y-value is 0. What is the coefficient of the squared term in the equation of this parabola? I don't know wh

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Question 1201024: The vertex of this parabola is at (1, 2). When the x-value is 0, the y-value is 0. What is the coefficient of the squared term in the equation of this parabola?
I don't know where or how to start, please help me.
Found 3 solutions by josgarithmetic, Theo, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
What kind of equation do you know for a parabola?
Recognize and the vertex is at point (h,k) ?
Use that!

You know the needed vertex and you know one other point (which is at the Origin).
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the vertex form of the equation is y = a * (x-h)^2 + k.
(h,k) is the vertex.
when the vertex is (1,2), this becomes y = a * (x-1)^2 + 2
when x = 0, y = 0.
therefore you get:
0 = a * (-1)^2 + 2
simplify to get:
0 = a + 2
solve for a to get:
a = -2
vertex form of the equation becomes y = -2 * (x-1)^2 + 2.
looks like the coefficient of the x^2 term is -2
the standard form of the equation is y = ax^2 + bx + c
to convert to this form, set y = 0 in the vertex form and solve.
you get 0 = -2 * (x-1)^2 + 2
simplify to get:
0 = -2 * (x^2 -2x + 1) + 2
simpify to get:
0 = -2*x^2 + 4x -2 + 2
simplify to get:
0 = -2x^2 + 4x.
that's the standard form of the equation.
your solution is that the coefficient of the x^2 term is -2.
here's the graph.



both forms of the equation show on the graph.
they both show the same figure on the graph, indicating that they are equivalent to each other.

here's a reference.

https://mathbitsnotebook.com/Algebra1/Quadratics/QDVertexForm.html
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
The vertex of this parabola is at (1, 2). When the x-value is 0, the y-value is 0. What is the coefficient of the squared term in the equation of this parabola? 

I don't know where or how to start, please help me.

Equation of a parabola: , where a is the coefficient of the squared term
                      ----- Substituting (0, 0) for (x, y), and (1, 2) for (h, k)
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