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

Video Solution

Solution Steps

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 Solution

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

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

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

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

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

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

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

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