How would you find the intercept for the equation y^2=2-3x-2x^2? I need the steps to understand
1 answer:
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.
You might be interested in
Check the picture below.
QUESTION 1
The given inequality is
We group like terms to get,
This implies that,
or
.
We simplify the inequality to get,
or
.
We can write this interval notation to get,
.
QUESTION 2
.
We group like terms to get,
.
We split the absolute value sign to get,
or
This implies that,
or
or
or
We can write this interval notation to get,
.
QUESTION 3
The given inequality is
We split the absolute value sign to obtain,
or
This simplifies to
and
and
and
and
We write this in interval form to get,
QUESTION 4
The given inequality is
We split the absolute value sign to get,
or
This simplifies to,
or
This implies that,
or
or
or
We write this in interval notation to get,