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In questions (1-5), write a possible equation for a polynomial whose graph has the
following horizontal intercepts. Check your equation using graphing technology.
1. (4,0)
2. (0,0) and (4, 0)
3. (-2, 0), (0, 0), and (4,0)
4. (-4, 0), (0, 0), and (2, 0)
5. (-5, 0), (1/2, 0), and (3, 0)

Respuesta :

MrRoyal

The possible equations for the polynomial are y = x - 4, y = -x^2 + 4x, y = x(x + 2)(x - 4), y = x(x + 4)(x - 2) and y = (x - 5)(x - 1/2)(x - 3)

How to write a possible equation for a polynomial whose graph has the given horizontal intercepts?

The horizontal intercept of a function is the x-intercepts of the function.

This means that the given intercepts are the x-intercepts of the function.

Using the above highlights, we have the following computations.

Polynomial function 1

Horizontal intercept = (4,0)

Rewrite as:

(x, y) = (4,0)

Because, we are given a point;

The polynomial function can be represented as a linear function

So, we have:

y = x - a

Substitute (x, y) = (4,0) in y = x - a

0 = 4 - a

Solve for a

a = 4

Substitute a = 4 in y = x - a

y = x - 4

Hence, the possible equation for the polynomial is y = x - 4

Polynomial function 2

Horizontal intercept = (0,0) and (4, 0)

Rewrite as:

(x, y) = (0,0) and (4, 0)

Because, we are given two points;

The polynomial function can be represented as a quadratic function

So, we have:

y = ax^2 + bx + c

Substitute (x, y) = (0,0) in y = ax^2 + bx + c

0 = a(0)^2 + (0)x + c

0 = 0 + 0 + c

Solve for

c = 0

Substitute c = 0 in y = ax^2 + bx + c

y = ax^2 + bx

Substitute (x, y) = (4,0) in y = ax^2 + bx

a(4)^2 + 4b = 0

16a + 4b = 0

Divide through by 4

4a + b = 0

Let b = 4

So, we have:

4a + 4 = 0

Solve for a

a = -1

Substitute a = -1 and b = 4 in y = ax^2 + bx

y = -x^2 + 4x

Hence, the possible equation for the polynomial is y = -x^2 + 4x

Polynomial function 3

Horizontal intercept = (-2, 0), (0, 0), and (4,0)

Rewrite as:

(x, y) = (-2, 0), (0, 0), and (4,0)

Here, we  have three points

The polynomial function can be represented as:

y = (x - a)(x - b)(x - c)

Where a, b and c are the values of x when y = 0 i.e. the given horizontal intercepts

So, we have:

y = (x + 2)(x - 0)(x - 4)

Evaluate the difference

y = (x + 2)(x)(x - 4)

Rewrite as:

y = x(x + 2)(x - 4)

Hence, the possible equation for the polynomial is y = x(x + 2)(x - 4)

Polynomial function 4

Horizontal intercept = (-4, 0), (0, 0), and (2, 0)

Rewrite as:

(x, y) = (-4, 0), (0, 0), and (2, 0)

Here, we have three points

The polynomial function can be represented as:

y = (x - a)(x - b)(x - c)

Where a, b and c are the values of x when y = 0 i.e. the given horizontal intercepts

So, we have:

y = (x + 4)(x - 0)(x - 2)

Evaluate the difference

y = (x + 4)(x)(x - 2)

Rewrite as:

y = x(x + 4)(x - 2)

Hence, the possible equation for the polynomial is y = x(x + 4)(x - 2)

Polynomial function 5

Horizontal intercept = (-5, 0), (1/2, 0), and (3, 0)

Rewrite as:

(x, y) = (-5, 0), (1/2, 0), and (3, 0)

Here, we have three points

The polynomial function can be represented as:

y = (x - a)(x - b)(x - c)

Where a, b and c are the values of x when y = 0 i.e. the given horizontal intercepts

So, we have:

y = (x - 5)(x - 1/2)(x - 3)

Hence, the possible equation for the polynomial is y = (x - 5)(x - 1/2)(x - 3)

Read more about polynomials at

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