84.7k views
13 votes
8. The graph of f(x) = 2x² - 5x is shown. Amanda

believes that the vertex of the graph is located at
(1.25, -3). Is she correct? If so, justify your thinking.
If not, give the correct vertex.

8. The graph of f(x) = 2x² - 5x is shown. Amanda believes that the vertex of the graph-example-1
User MiuMiu
by
7.8k points

1 Answer

9 votes

Answer: Amanda is not correct

The vertex is at (1.25, -3.125)

=========================================================

Reason:

The x intercepts are 0 and 2.5

This is where the graph crosses the x axis. If we plugged in either x = 0 or x = 2.5, then we'd get f(x) = 0.

Find the midpoint of those values mentioned. Add them up, and divide by 2 to get the midpoint to be (0+2.5)/2 = 1.25

This is the x coordinate of the vertex.

Then plug that into the function to find the corresponding y coordinate of the vertex.

f(x) = 2x^2 - 5x

f(1.25) = 2(1.25)^2 - 5(1.25)

f(1.25) = -3.125

The vertex is located at (1.25, -3.125)

Amanda's x coordinate is correct, but the y coordinate isn't. Though her y coordinate isn't too far off.

I think I can see why she went with y = -3 since the lowest part of the graph is around this area. However, the lowest part of the parabola dips a tiny bit below y = -3. This is why it's better to use the equation rather than solely rely on the graph alone.

User Harry
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.