This math topic focuses on utilizing the vertex form of a quadratic equation to determine the correct equation based on a given vertex and the direction the parabola opens (up or down). Each problem provides a vertex point and specifies whether the parabola opens upward or downward. Students are then asked to select the correct quadratic function from a set of multiple-choice answers that represent the equation in vertex form. This helps reinforce understanding of how alterations in the vertex form \( y = a(x-h)^2 + k \) affect the graph's shape and position.

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Quadratics Vertex Form - Vertex to Equation Worksheet

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Quadratics Vertex Form - Vertex to Equation
1
(-2, 1), opening down
What function would have this vertex?
a A LaTex expression showing y=-1(x-2) to the power of 2 +1
b A LaTex expression showing y=-1(x+2) to the power of 2 +1
c A LaTex expression showing y=-1(x+2) to the power of 2 -1
d A LaTex expression showing y=(x+2) to the power of 2 -1
2
(-1, -1), opening up
What function would have this vertex?
a A LaTex expression showing y=(x+1) to the power of 2 +1
b A LaTex expression showing y=-1(x+1) to the power of 2 -1
c A LaTex expression showing y=(x-1) to the power of 2 -1
d A LaTex expression showing y=(x+1) to the power of 2 -1
3
(-3, 1), opening down
What function would have this vertex?
a A LaTex expression showing y=1.5(x+3) to the power of 2 +1
b A LaTex expression showing y=-1.5(x+3) to the power of 2 +1
c A LaTex expression showing y=1.5(x+3) to the power of 2 -1
d A LaTex expression showing y=-1.5(x-3) to the power of 2 +1
4
(-4, -4), opening down
What function would have this vertex?
a A LaTex expression showing y=-1(x+4) to the power of 2 -4
b A LaTex expression showing y=(x+4) to the power of 2 +4
c A LaTex expression showing y=-1(x-4) to the power of 2 -4
d A LaTex expression showing y=(x-4) to the power of 2 +4
5
(3, -2), opening down
What function would have this vertex?
a A LaTex expression showing y=-1.5(x-3) to the power of 2 +2
b A LaTex expression showing y=-1.5(x-3) to the power of 2 -2
c A LaTex expression showing y=-1.5(x+3) to the power of 2 -2
d A LaTex expression showing y=1.5(x-3) to the power of 2 -2
6
(4, -4), opening down
What function would have this vertex?
a A LaTex expression showing y=-1(x-4) to the power of 2 +4
b A LaTex expression showing y=-1(x-4) to the power of 2 -4
c A LaTex expression showing y=(x+4) to the power of 2 -4
d A LaTex expression showing y=-1(x+4) to the power of 2 -4
7
(4, -4), opening up
What function would have this vertex?
a A LaTex expression showing y=-1(x-4) to the power of 2 -4
b A LaTex expression showing y=(x+4) to the power of 2 +4
c A LaTex expression showing y=(x-4) to the power of 2 -4
d A LaTex expression showing y=(x-4) to the power of 2 +4
8
(4, 3), opening down
What function would have this vertex?
a A LaTex expression showing y=(x-4) to the power of 2 +3
b A LaTex expression showing y=-1(x-4) to the power of 2 +3
c A LaTex expression showing y=-1(x-4) to the power of 2 -3
d A LaTex expression showing y=-1(x+4) to the power of 2 +3