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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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4.697 Answers
1. To find the y-intercept, set x = 0 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 0 = 3x^2 - 21x + 30 x
- 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) (5, 0)
Therefore, the final intercepts are:
x \text{-intercepts: } (2, 0) \text{ and } (5, 0)
y \text{-intercept: } (0, 30)
So, the y-intercept is
2. To find the x-intercepts, set
- Factor the quadratic equation:
- Solve the factorized equation:
- Find the zeros:
So, the x-intercepts are
Therefore, the final intercepts are:
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