Locate Point C on f(x) = -x² + 5x + 6: Quadratic Graph Analysis

The following function has been graphed below:

f(x)=−x2+5x+6 f(x)=-x^2+5x+6

Calculate point C.

BBBAAACCC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the coordinates of point C
00:03 Point C is the vertex point so we want to find it
00:07 We'll use the formula to calculate the vertex point
00:10 Let's look at the function coefficients
00:16 We'll substitute appropriate values and solve for X
00:26 This is the X value at point C
00:32 Now we'll substitute this value in the function to find Y value at point C
00:37 Let's calculate and solve
00:52 This is the Y value at point C
00:56 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The following function has been graphed below:

f(x)=−x2+5x+6 f(x)=-x^2+5x+6

Calculate point C.

BBBAAACCC

2

Step-by-step solution

To answer the question, we must first remember the formula for finding the vertex of a parabola:

Now let's substitute the known data into the formula:

-5/2(-1)=-5/-2=2.5

In other words, the x-coordinate of the vertex of the parabola is found when the X value equals 2.5.

Now let's substitute this into the parabola equation to find the Y value:

-(2.5)²+5*2.5+6= 12.25

Therefore, the coordinates of the vertex of the parabola are (2.5, 12.25).

3

Final Answer

(212,1214) (2\frac{1}{2},12\frac{1}{4})

Practice Quiz

Test your knowledge with interactive questions

The following function has been plotted on the graph below:

\( f(x)=x^2-8x+16 \)

Calculate point C.

CCC

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