Find a formula for the given linear function, h(x). The graph of h intersects the graph of y = x² at x = -4 and x = 5. NOTE: Enter the exact answer. h(x) = ||
Find a formula for the given linear function, h(x). The graph of h intersects the graph of y = x² at x = -4 and x = 5. NOTE: Enter the exact answer. h(x) = ||
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Problem Statement:**
Find a formula for the given linear function, \( h(x) \).
The graph of \( h \) intersects the graph of \( y = x^2 \) at \( x = -4 \) and \( x = 5 \).
**NOTE:** Enter the exact answer.
**Solution:**
To solve the problem, we need to find the equation of the line \( h(x) \) that intersects the parabola \( y = x^2 \) at the given x-values: \( x = -4 \) and \( x = 5 \).
1. Calculate the y-values where the parabola intersects at these x-values:
\[
y(-4) = (-4)^2 = 16
\]
\[
y(5) = (5)^2 = 25
\]
2. The points of intersection are \((-4, 16)\) and \((5, 25)\).
3. Find the slope (\(m\)) of the line connecting these points:
\[
m = \frac{25 - 16}{5 - (-4)} = \frac{9}{9} = 1
\]
4. Use the point-slope form to find the equation of the line. We'll use the point \((-4, 16)\):
\[
y - 16 = 1(x + 4)
\]
Simplify:
\[
y = x + 4 + 16
\]
\[
y = x + 20
\]
Thus, the equation for \( h(x) \) is:
\[ h(x) = x + 20 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92ab3c20-a3cd-4c1e-8775-52ac5ed4d4cf%2F0f668f2e-22c6-42e3-952f-7ece5a4131de%2Fzeab2m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find a formula for the given linear function, \( h(x) \).
The graph of \( h \) intersects the graph of \( y = x^2 \) at \( x = -4 \) and \( x = 5 \).
**NOTE:** Enter the exact answer.
**Solution:**
To solve the problem, we need to find the equation of the line \( h(x) \) that intersects the parabola \( y = x^2 \) at the given x-values: \( x = -4 \) and \( x = 5 \).
1. Calculate the y-values where the parabola intersects at these x-values:
\[
y(-4) = (-4)^2 = 16
\]
\[
y(5) = (5)^2 = 25
\]
2. The points of intersection are \((-4, 16)\) and \((5, 25)\).
3. Find the slope (\(m\)) of the line connecting these points:
\[
m = \frac{25 - 16}{5 - (-4)} = \frac{9}{9} = 1
\]
4. Use the point-slope form to find the equation of the line. We'll use the point \((-4, 16)\):
\[
y - 16 = 1(x + 4)
\]
Simplify:
\[
y = x + 4 + 16
\]
\[
y = x + 20
\]
Thus, the equation for \( h(x) \) is:
\[ h(x) = x + 20 \]
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