Calculate Point B on the Graph of f(x) = x² - 6x + 8

The following function has been graphed below.

f(x)=x26x+8 f(x)=x^2-6x+8

Calculate point B.

BBB

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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 B
00:03 Point B is the vertex point, so we want to find it
00:08 We'll use the formula to calculate the vertex point
00:11 Let's identify the function coefficients
00:17 We'll substitute appropriate values and solve for X
00:25 This is the X value at point C
00:30 Now we'll substitute this value in the function to find the Y value at point C
00:35 Let's calculate and solve
00:41 This is the Y value at point C
00:45 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

The following function has been graphed below.

f(x)=x26x+8 f(x)=x^2-6x+8

Calculate point B.

BBB

2

Step-by-step solution

To calculate point B, we should determine the vertex of the quadratic function f(x)=x26x+8 f(x) = x^2 - 6x + 8 .

The x-coordinate of the vertex can be found using the formula x=b2a x = -\frac{b}{2a} .

In our equation, we have a=1 a = 1 and b=6 b = -6 , therefore:

x=62×1=62=3 x = -\frac{-6}{2 \times 1} = \frac{6}{2} = 3

Next, we substitute x=3 x = 3 back into the function to find the y-coordinate:

f(3)=326×3+8=918+8=1 f(3) = 3^2 - 6 \times 3 + 8 = 9 - 18 + 8 = -1

Thus, the vertex, which is point B, is (3,1) (3, -1) .

Therefore, the solution indicates that point B is at (3,1) (3, -1) .

3

Final Answer

(3,1) (3,-1)

Practice Quiz

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The following function has been graphed below:

\( f(x)=x^2-6x \)

Calculate point C.

CCCAAABBB

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