# Find x-and y-Intercepts of Each Graph

Discussion in 'Other Pre-University Math' started by nycmathguy, Aug 11, 2021.

1. ### nycmathguy

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Set 1.5
David Cohen
Questions 22 & 24

Exercises 21–24, each figure shows the graph of an equation. Find the x- and y-intercepts of the graph. If an intercept involvesa radical, give both the radical form of the answer and a calcu-
lator approximation rounded to two decimal places. (Check to see that your answer is consistent with the given figure.)

Let me see.

To find the x-intercept, let y = 0 and solve for x.
To find the y-intercept, let x = 0 and solve for y.

Yes? nycmathguy, Aug 11, 2021
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2. ### MathLover1

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yes

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3. ### nycmathguy

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Not so bad. I will show my work when time allows.

nycmathguy, Aug 11, 2021
4. ### nycmathguy

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[QUOTE="MathLover1,

Question 22

y = x^3 + x^2 - 3x

Let x = 0

y = (0)^3 + (0)^2 - 3(0)

y = 0.

Our y-intercept is found at the point (0, 0) aka the origin. The graph shows this to be true.

Let y = 0

0 = x^3 + x^2 - 3x

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

Set each factor to 0 and solve for x.

I see that x = 0 is one of the x-intercept found at the point (0,0). This graph shows this to be true.

x^2 + x - 3 = 0

By the quadratic formula, I found two more x-intercepts.

x = -(1/2) - sqrt13}/2

x = sqrt{13}/2 - (1/2)

The graph shows this to be true as well.

nycmathguy, Aug 11, 2021
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5. ### nycmathguy

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Question 24

x^3 + x^2 y = 12

Let x = 0

(0)^3 + (0)^2 y = 12

0 + 0 does not equal 12. I conclude there are no y-intercepts. The graph shows this to be true.

Let y = 0

x^3 + x^2 (0) = 12

x^3 = 12

Let cr = cube root

cr{x^3} = cr{12}

x = 2.2894284851

Rounding to two decimal places, I get 2.29.
The graph shows this to be true as the graph crosses the x-axis slightly to the right of 2.

You say?

nycmathguy, Aug 11, 2021
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6. ### MathLover1

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correct

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