The vertex of the parabola indicates the highest or maximum point of a sad-faced parabola, and the lowest or minimum point of a happy-faced parabola.

Question Types:

The vertex of the parabola indicates the highest or maximum point of a sad-faced parabola, and the lowest or minimum point of a happy-faced parabola.

**First step:** We will find the $X$ of the vertex according to the formula $x=\frac{(-b)}{2a}$

**Second step:** We will place the $X$ of the vertex we have found into the original parabola equation to find the $Y$ of the vertex.

**First step:** Find two points of intersection of the parabola with the $X$ axis using the quadratic formula.

**Second step:** Find the $X$ of the vertex: the point that is exactly between two points of intersection. The calculation will be done through the average of two $X$s of the intersection points.

**Third step:** Place the $X$ of the vertex we have found into the original parabola equation to solve for the $Y$ of the vertex.

Question 1

The following function has been graphed below:

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

Calculate point C.

Question 2

The following function has been graphed below.

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

Calculate point B.

Question 3

The following function has been graphed below.

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

Calculate point C.

Question 4

The following function has been graphed below:

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

Calculate point C.

Question 5

Find the vertex of the parabola

\( y=x^2-6 \)

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.

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

Calculate point C.

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

The following function has been graphed below:

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

Calculate point C.

$(4,0)$

Find the vertex of the parabola

$y=x^2-6$

$(0,-6)$

Question 1

Find the vertex of the parabola

\( y=x^2 \)

Question 2

Find the vertex of the parabola

\( y=(x-3)^2 \)

Question 3

Find the vertex of the parabola

\( y=(x+1)^2 \)

Question 4

Find the vertex of the parabola

\( y=(x-1)^2-1 \)

Question 5

Find the vertex of the parabola

\( y=(x+1)^2-1 \)

Find the vertex of the parabola

$y=x^2$

$(0,0)$

Find the vertex of the parabola

$y=(x-3)^2$

$(3,0)$

Find the vertex of the parabola

$y=(x+1)^2$

$(-1,0)$

Find the vertex of the parabola

$y=(x-1)^2-1$

$(1,-1)$

Find the vertex of the parabola

$y=(x+1)^2-1$

$(-1,-1)$

Question 1

Find the vertex of the parabola

\( y=(x-3)^2-1 \)

Question 2

Find the vertex of the parabola

\( y=x^2+3 \)

Question 3

Find the vertex of the parabola

\( y=(x-6)^2+1 \)

Question 4

Find the vertex of the parabola

\( y=(x+2)-2 \)

Question 5

Find the vertex of the parabola

\( y=(x+2)-3 \)

Find the vertex of the parabola

$y=(x-3)^2-1$

$(3,-1)$

Find the vertex of the parabola

$y=x^2+3$

$(0,3)$

Find the vertex of the parabola

$y=(x-6)^2+1$

$(6,1)$

Find the vertex of the parabola

$y=(x+2)-2$

$(-2,-2)$

Find the vertex of the parabola

$y=(x+2)-3$

$(-2,-3)$