How would you find the intercept for the equation y^2=2-3x-2x^2? I need the steps to understand

Mathematics

1 answer:

krek1111 [17]3 years ago

3 0

9514 1404 393

Answer:

x-intercepts: -2, +1/2
y-intercepts: ±√2

Step-by-step explanation:

You always find the intercepts by setting the known coordinate to its known value and solving for the value of the unknown coordinate.

An x-intercept is always found on the line y=0. Setting y=0 and solving for x, we find ...

0 = 2 -3x -2x^2

x^2 +3/2x -1 = 0 . . . . . . . . . . . . . . . . divide by -2

(x2^2 +3/2x +(3/4)^2) -1 -(3/4)^2 = 0 . . . . . complete the square

(x +3/4)^2 = 25/16 . . . . . add 25/16 and write as a square

x +3/4 = ±5/4 . . . . . . . take the square root

x = -3/4 ±5/4 = -8/4, +2/4

The x-intercepts are -2 and +1/2.

A y-intercept is always found on the line x=0. Setting x=0 and solving for y, we find ...

y^2 = 2 -0 -0

y = ±√2

The y-intercepts are -√2 and +√2.

_____

A graphing calculator can give you a good idea of what the intercepts are.

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laila [671]

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Step-by-step explanation:

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I often, personally, find it easier to think of these questions coming from a function-graph standpoint, where you have x (domain) and y (range). Logical thinking immediately tells you the time would fall on the x-axis, aka the independent variable. Setting logic aside, look at the question from a literal factual perspective. Jill chucks her drum wand up in the air, much like an angry base-ball player would a bat, and she's already determined her routine will take place in a TWO SECOND time frame before the wand comes BACK DOWN and clobbers Jill on the head (unless she catches it, ofc). However it may just be lights out for Jill, because the DEPENDENT variable is the height. If Jill chucks it too high, she's gonna be standing waiting for it to come down. If she's short, she's going to get KO'd by an in-animate object mid-twirl.

The baton NEEDS to be in the air for a total of 2 seconds, thus making the height dependent upon the time, much like Jill is dependent upon the laws of physics and good timing to prevent getting cold-clocked.

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