Question

Find all point(s) of intersection of the line y = 4x and the parabola y = x^2 - 2x + 9.

Answer 1

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.

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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.