Grade 12 Math Conics?
I got a question on Math 30 for conics. The positive y-intercept, to the nearest hundredth of the parabola y2-2x+3y-7=0. I looked in my answer book to figure out how to solve it and it confused me more. Here are the steps: 1. Let x=0, y2+3y-7=0. Then y=-3 +.-|9+28|/2
Note: |9+28| stands for square root of 9+28
you get an answer of -4.54 and 1.54. I just don't understand the steps on how they managed to get rid of y2 and managed to get the number 9 and 28. If someone can explain it in further detail would be helpful. Note: it's y=-3, + and - Square root 9 + 28 divided by 2. In case you are confused.
Comments
It's called the quadratic formula, and you (should have) learned it a few years ago. If ax^2 + bx + c = 0, then x = [-b +/- sqrt(b^2 - 4ac)]/(2a). You're using y's instead of x's, and a=1, b=3, and c=7. So the b^2 becomes 9 and the -4ac becomes +28.
It comes from the idea of completing the squares to solve a quadratic, but most people just memorize the formula instead!
y² - 2x + 3y - 7 = 0
- 2x = - y² - 3y + 7
2x = y² - 3y - 7
x = 1/2 y² - 3/2 x - 7/2
y-int.: x = 0:
1/2 y² - 3/2 y - 7/2 = 0
2(1/2 y²) - 2(3/2 y) - 2(7/2) = 2(0)
y² - 3y - 7 = 0
y² - 3y = 7
y² - 3y + 2.25 = 7 + 2.25
(y - 1.5)² = 9.25
y - 1.5 = √9.25
y = 1.5 ± 3.04
Positive y-int.:
y = 1.5 + 3.04
y = 4.54
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