Question

In Exercises 105-108, determine the $x$-and $y$-intercepts, if they exist, of the graph of each equation. $$ x=2(y-3)^{2}+6 $$

Name: Problem 107, Chapter 10: Intermediate Algebra for College Students
Uploaded: 2021-04-30T19:36:51-08:00
Duration: 2 min 45 s
Channel: Raushan Kumar
Description: In Exercises 105-108, determine the x-and y-intercepts, if they exist, of the graph of each equation. x=2(y-3)^2+6

   In Exercises 105-108, determine the $x$-and $y$-intercepts, if they exist, of the graph of each equation.
$$
x=2(y-3)^{2}+6
$$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 10, Problem 107

Instant Answer

Solved by Expert Raushan Kumar

04/30/2021

Step 1

To do this, we'll set y = 0 and solve for x. x = 2(0 - 3)^2 + 6 x = 2(-3)^2 + 6 x = 2(9) + 6 x = 18 + 6 x = 24 So the x-intercept is (24, 0). Now, let's find the y-intercept. To do this, we'll set x = 0 and solve for y. 0 = 2(y - 3)^2 + 6 We'll first subtract Show more…

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In Exercises 105-108, determine the $x$-and $y$-intercepts, if they exist, of the graph of each equation. $$ x=2(y-3)^{2}+6 $$

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Key Concepts

Y-intercept

The y-intercept is the point where the graph crosses the y-axis, which happens when x is zero. To find it, x is set to zero in the equation and the corresponding y values are obtained by solving the resulting equation. In some cases, there may be no real y-intercepts if the resulting equation does not yield a solution.

Graph Orientation

The given equation represents a parabola where x is expressed in terms of y. This indicates that the parabola opens horizontally rather than vertically. Recognizing the orientation of the graph is critical for correctly finding and interpreting the intercepts.

X-intercept

The x-intercept is the point where the graph crosses the x-axis, which occurs when the value of y is zero. To find the x-intercept, y is substituted with zero in the equation, and then x is solved from the resulting equation.

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