Calculate Point C on the Quadratic Graph of f(x)=x²-6x

Video Solution

Solution Steps

00:00 Find the coordinates of point C

00:03 Point C is the vertex point so we want to find it

00:06 Let's look at the function coefficients

00:11 We'll use the formula to calculate the vertex point

00:14 We'll substitute appropriate values and solve for X

00:28 This is the X value at point C

00:31 Now we'll substitute this value in the function to find the Y value at point C

00:40 Let's calculate and solve

00:44 This is the Y value at point C

00:49 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll calculate the vertex of the parabola given by the quadratic function $f(x) = x^2 - 6x$ .

Step 1: Identify the coefficients $a = 1$ and $b = -6$ .
Step 2: Use the vertex formula $x = -\frac{b}{2a}$ to find the x-coordinate of the vertex.
Step 3: Substitute the calculated x-coordinate back into the function to find the y-coordinate.

Now, let's compute:

Step 1: The function is $f(x) = x^2 - 6x$ with coefficients $a = 1$ and $b = -6$ .

Step 2: Apply the vertex formula: $x = -\frac{-6}{2 \times 1} = \frac{6}{2} = 3$ .

Step 3: For $x = 3$ , substitute into $f(x)$ to find the y-coordinate:

$f(3) = (3)^2 - 6 \times 3 = 9 - 18 = -9$ .

Therefore, the coordinates of the point C, which is the vertex, are $(3, -9)$ .

The correct answer is $(3, -9)$ , which corresponds to the given correct choice.