Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

1. The zeros of the quadratic equation [tex]x^2 + 4x = -2x + 16[/tex] are [tex]x = -8[/tex] and [tex]x = 2[/tex].

What does this tell you about the graph of this quadratic function?

A. The parabola crosses the [tex]x[/tex]-axis at [tex]x = -8[/tex] and [tex]x = 2[/tex].

B. The parabola crosses the [tex]x[/tex]-axis at [tex]x = -8[/tex] and [tex]x = 2[/tex], but you can ignore the zero [tex]x = -8[/tex] because it is negative.

C. The parabola does not touch or cross the [tex]x[/tex]-axis.

D. The parabola touches the [tex]x[/tex]-axis only at [tex]x = 2[/tex].

Sagot :

GinnyAnswer
To understand what the zeros of the quadratic equation [tex]\(x^2 + 4x = -2x + 16\)[/tex] tell us about its graph, let's start by rewriting the equation and analyzing its solution.

First, simplify and standardize the quadratic equation:
[tex]\[ x^2 + 4x + 2x - 16 = 0 \][/tex]
Combine like terms:
[tex]\[ x^2 + 6x - 16 = 0 \][/tex]

To find the zeros of the quadratic equation, we solve [tex]\(x^2 + 6x - 16 = 0\)[/tex]. The solutions to this equation are the values of [tex]\(x\)[/tex] where the quadratic function intersects the x-axis.

The zeros (roots) of this quadratic function are [tex]\(x = -8\)[/tex] and [tex]\(x = 2\)[/tex].

1. Zeros or Roots: The solutions, [tex]\(x = -8\)[/tex] and [tex]\(x = 2\)[/tex], are the x-intercepts of the parabola. This means the parabola crosses the x-axis at these points.

2. Graph Behavior: The x-intercepts tell us critical points where the graph touches or crosses the x-axis.

Based on this information, let's discuss each of the provided statements:

- The parabola crosses the x-axis at [tex]\(x = -8\)[/tex] and [tex]\(x = 2\)[/tex]:
This statement is correct. Since both [tex]\(x = -8\)[/tex] and [tex]\(x = 2\)[/tex] are zeros of the quadratic equation, the parabola crosses the x-axis at these two points.

- The parabola crosses the x-axis at [tex]\(x = -8\)[/tex] and [tex]\(x = 2\)[/tex], but you can ignore the zero [tex]\(x = -8\)[/tex] because it is negative:
This statement is incorrect. Both zeros are important in understanding the behavior of the parabola. Ignoring one of them because it's negative is not a valid mathematical practice.

- The parabola does not touch or cross the x-axis:
This statement is incorrect. The zeros [tex]\(x = -8\)[/tex] and [tex]\(x = 2\)[/tex] specifically indicate the points where the parabola touches or crosses the x-axis.

- The parabola touches the x-axis only at [tex]\(x = 2\)[/tex]:
This statement is incorrect. The parabola touches or crosses the x-axis at both [tex]\(x = -8\)[/tex] and [tex]\(x = 2\)[/tex].

Therefore, the correct conclusion is:
The parabola crosses the x-axis at [tex]\(x = -8\)[/tex] and [tex]\(x = 2\)[/tex].
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.