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Determine the x-intercept and y-intercept: y = 3x^2 - 21x + 30

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Answer to a math question Determine the x-intercept and y-intercept: y = 3x^2 - 21x + 30

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Bud

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96 Answers

1. To find the y-intercept, set

x = 0

in the equation

y = 3x^2 - 21x + 30

y = 3(0)^2 - 21(0) + 30 = 30

So, the y-intercept is

(0, 30)

.

2. To find the x-intercepts, set

y = 0

in the equation

0 = 3x^2 - 21x + 30

and solve for

:
- Factor the quadratic equation:

3x^2 - 21x + 30 = 0

3(x^2 - 7x + 10) = 0

x^2 - 7x + 10 = 0

- Solve the factorized equation:

(x - 2)(x - 5) = 0

- Find the zeros:

x = 2 \text{ or } x = 5

So, the x-intercepts are

(2, 0)

and

(5, 0)

.

Therefore, the final intercepts are:

x \text{-intercepts: } (2, 0) \text{ and } (5, 0)

y \text{-intercept: } (0, 30)

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Determine the x-intercept and y-intercept: y = 3x^2 - 21x + 30

Answer to a math question Determine the x-intercept and y-intercept: y = 3x^2 - 21x + 30

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