Question

Without sketching the graph, find the x-intercepts and y-intercepts of the graph of the equation y=x²-x-6 What is/are the x-intercept(s)? Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The x-intercept(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OB. There are no x-intercepts What is/are the y-intercept(s)? Select the correct choice below and, if necessary, fill in the answer box within your choice O A. The y-intercept(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) OB. There are no y-intercepts Click to select and enter your answer(s)

Answer 1

Given the equation:

$y=x^2-x-6$

Let's find the x-intercepts and the y-intercepts of the graph.

• x-intercept:

The x-intercept are the points where the parabola crosses the x-axis. At x-intercept the y-value is zero.

To find the x-intercepts, substitute 0 for y and solve for x.

We have:

$0=x^2-x-6$

Rewrite the equation:

$x^2-x-6=0$

Factor the left hand side of the equation:

$(x-3)(x+2)=0$

Equate each factor to zero:

x - 3 = 0

Add 3 to both sides:

x - 3 + 3 = 0 + 3

x = 3

x + 2 = 0

Subtract 2 from both sides:

x + 2 - 2 = 0 - 2

x = -2

Therefore, the x-intercepts are:

3, -2

• y-intercept:

The y-intercept is the point where the parabola crosses the y-axis. The x-value at the y-intercept is zero.

To find the y-intercept, substitute 0 for x and solve:

$\begin{gathered} y=0^2-0-6 \\ \\ y=-6 \end{gathered}$

Therefore, the y-intercept is -6.

In point form:

x-intercept: (3, 0), (-2, 0)

y-intercept: (0, -6)

ANSWER:

A. The x-intercepts are (3, 0), (-2, 0)

A. The y-intercept is (0, -6)