Jen knows that (-1, 41) and (5, 41) lie on a parabola defined by the equation y = 4x² - 16x + 21. What are the coordinates of the vertex?

Jen knows that (-1, 41) and (5, 41) lie on a parabola defined by the equation y = 4x² - 16x + 21. What are the coordinates of the vertex?

Question
Functions
asked 2020-10-25
Jen knows that (-1, 41) and (5, 41) lie on a parabola defined by the equation y = 4x² - 16x + 21. What are the coordinates of the vertex?

Answers (1)

2020-10-26
The vertex of a parabola lies on the axis of symmetry which divides the parabola into two mirror images. Notice that the two points are reflection of each other about a vertical line since they have the same yy-coordinate. This means that the average of their xx-coordinates is the xx-coordinate of the vertex:
\(\displaystyle{x}=\frac{{−{1}+{5}}}{{2}}={2}\)
To find the y-coordinate of the vertex, substitute x=2 to the equation:
\(\displaystyle{y}={4}{\left({2}\right)}^{{2}}−{16}{\left({2}\right)}+{21}={5}\)
So, the vertex is at:
(2,5)
0

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