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

Question

The following function has been graphed below:

$f(x)=-x^2+5x+6$

Calculate point C.

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

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).

$(2\frac{1}{2},12\frac{1}{4})$