k(x)=(x−2)2−7
Step 2 of 4 :  Find the x-intercepts, if any. Express the intercept(s) as ordered pair(s).

To find the x-intercepts of the function \( k(x) = (x - 2)^2 - 7 \), we need to set \( k(x) \) equal to 0 and solve for \( x \).

### Step 1: Set the function equal to zero
\[
(x - 2)^2 - 7 = 0
\]

### Step 2: Solve for \( x \)
First, add 7 to both sides of the equation:
\[
(x - 2)^2 = 7
\]

Next, take the square root of both sides:
\[
x - 2 = \pm \sqrt{7}
\]

Finally, add 2 to both sides to solve for \( x \):
\[
x = 2 \pm \sqrt{7}
\]

So the two solutions for \( x \) are:
\[
x = 2 + \sqrt{7} \quad \text{and} \quad x = 2 - \sqrt{7}
\]

### Step 3: Write the x-intercepts as ordered pairs
The x-intercepts are:
\[
(2 + \sqrt{7}, 0) \quad \text{and} \quad (2 - \sqrt{7}, 0)
\]

These are the points where the graph of the function intersects the x-axis.

Would you like more details or have any questions about this? Here are some related questions you might be interested in:

1. How do you find the y-intercept of the function \( k(x) = (x - 2)^2 - 7 \)?
2. What is the vertex of the function \( k(x) = (x - 2)^2 - 7 \)?
3. How do you graph the function \( k(x) = (x - 2)^2 - 7 \) using its vertex and intercepts?
4. What is the axis of symmetry for the function \( k(x) = (x - 2)^2 - 7 \)?
5. How does the graph of \( k(x) = (x - 2)^2 - 7 \) compare to the graph of \( k(x) = x^2 \)?

**Tip:** When solving quadratic equations, don't forget to consider both the positive and negative square roots when taking the square root of both sides.

Learn how to find the x-intercepts of the quadratic function (x - 2)^2 - 7 using step-by-step solutions. This problem covers quadratic equations, roots of equations, and square root calculations. Suitable for high school students studying algebra and quadratic functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation