Find all point(s) of intersection of the line y = 4x and the parabola y = x^2 - 2x + 9.
1 answer:
Answer:
A) (3, 12)
Step-by-step explanation:
For such a problem, I like to use a graphing calculator. It shows the answer quickly without a lot of fuss.
_____
If you want to solve this analytically, set the difference in y-values equal to zero and solve the resulting quadratic in the usual way. This will give the x-value at which the y-values are equal. (After we find x, we still need to find y.)
... y - y = 0
... x² -2x +9 -4x = 0
... x² -6x +9 = 0 . . . . . . collect terms. Recognize this as a perfect square.
... (x -3)² = 0
... x = 3 is the solution to this
... y = 4x = 4·3 = 12
The point on each of the given curves is (x, y) = (3, 12). The line is tangent to the parabola there, so there is only one point of intersection.
You might be interested in
9514 1404 393
Answer:
D
Step-by-step explanation:
Solve x = f(y) for y.
x = ∛(y/9) -4
x +4 = ∛(y/9) . . . . . add 4
(x +4)³ = y/9 .. . . . . cube
9(x +4)³ = y . . . . . . multiply by 9
The inverse function is ...
f⁻¹(x) = 9(x +4)³ . . . . . matches the last choice
