Describe the Relationships Among Solutions of an Equation, Zeros of a Function

How are solutions, roots, x​ -intercepts, and zeros related?

• The solutions are the y​ -values that correspond to the roots, x​ -intercepts, and zeros of an equation.

• The solutions are the roots, and are the y​ -values that correspond to the  x​ -intercepts and the zeros of an equation.

• There are two roots or zeros for every  x​ -intercept or solution of an equation.

• The solutions are the same as the roots of the equation and are the same as the x​ -intercepts or zeros of the related equation.

Estimate the intercepts of the graph of the function.

• x - intercepts:

  (1, 0) and (3, 0)

  y - intercept:

  (0, -3)

• x - intercepts:

  (1, 0) and (3, 0)

  y - intercept:

  (-3, 0)

• x - intercepts:

  (1, 0) and (3, 0)

  y - intercept:

  (3, 0)

• x - intercepts:

  (1, 0) and (-3, 0)

  y - intercept:

  (3, 0)

How can you use a graph to determine the number of real solutions of a quadratic equation?

Evaluate responses using AI:

OFF

A ​ (a)   of an ​ (b)   is a ​ (c)   of the equation. You can use various methods to ​ (d)   ​ (e)  

• root

• equation

• solution

• solve

• quadratic equations.

What are the roots of this function?

• There are none.

• -3

• 3

• -3 and 3

What are the roots of this quadratic function?

What are the other names for x-intercepts? ​ (a)   ​ (b)  

• roots

• zeros

• domains

• equations

What are the zeros, roots and solutions for this quadratic function?

• -2, -2, and 1

• -2 and 1

• 1 and 2

• -3 and 2

What are the zeros of this function?

Find the zeros of the function above.

*remember to change n to x in Desmos*

• -4, 2

• -2, 4

• -16

• -4