The Vertex of the Parabola: Finding a stationary point

The following function has been graphed below.

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

Calculate point C.

To solve the question, let's recall the formula for finding the vertex of a parabola:

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 and 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).

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

The following function has been graphed below:

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

Calculate point C.

$(3,-9)$

The following function has been graphed below.

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

Calculate point B.

$(3,-1)$

The following function has been graphed below:

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

Calculate point C.

$(4,0)$