Zeros of a Fuction: Finding a stationary point

Calculating geometric shapes Linking function properties to its representation

Question 1

The following function has been plotted on the graph below:

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

Calculate point C.

Question 2

The following function has been graphed below:

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

Calculate points A and B.

Question 3

The following function has been graphed below:

$$ f(x)=x^2-3x-4 $$

Calculate points A and B.

Question 4

The following function has been graphed below:

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

Calculate points A and B.

$$

Question 5

The following function has been graphed below:

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

Calculate points A and B.

Examples with solutions for Zeros of a Fuction: Finding a stationary point

Exercise #1

The following function has been plotted on the graph below:

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

Calculate point C.

Video Solution

Step-by-Step Solution

To solve the exercise, first note that point C lies on the X-axis.

Therefore, to find it, we need to understand what is the X value when Y equals 0.

Let's set the equation equal to 0:

0=x²-8x+16

We'll use the preferred method (trinomial or quadratic formula) to find the X values, and we'll discover that

X=4

Answer

$(4,0)$

Exercise #2

The following function has been graphed below:

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

Calculate points A and B.

Video Solution

Answer

$(-1,0),(6,0)$

Exercise #3

The following function has been graphed below:

$f(x)=x^2-3x-4$

Calculate points A and B.

Video Solution

Answer

$A(-1,0),B(4,0)$

Exercise #4

The following function has been graphed below:

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

Calculate points A and B.

Video Solution

Answer

$(1,0),(5,0)$

Exercise #5

The following function has been graphed below:

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

Calculate points A and B.

Video Solution

Answer

$(2,0),(4,0)$

Question 1

The following function has been graphed below:

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

Calculate points A and B.

Question 2

The following function has been graphed below:

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

Calculate point A.

Question 3

The following function has been graphed below:

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

Calculate point C.

Question 4

The following function has been graphed below:

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

Calculate point C.

Exercise #6

The following function has been graphed below:

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

Calculate points A and B.

Video Solution

Answer

$(6,0),\lparen0,0)$

Exercise #7

The following function has been graphed below:

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

Calculate point A.

Video Solution

Answer

$(0,16)$

Exercise #8

The following function has been graphed below:

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

Calculate point C.

Video Solution

Answer

$(0,5)$

Exercise #9

The following function has been graphed below:

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

Calculate point C.

Video Solution

Answer

$(0,8)$