Question

For what value(s) of k do the parabolas y=x²+2x-k and y=3x-1 intersect at exactly two points?

Answer 1

At `k = 7/9`

To solve this question, you can try to get the value of the functions when y is zero. This gives you the value of x from the linear function which you can substitute into the quadratic one to get the value of k

Explanation:

From `y = 3x - 1`, if `y = 0` then `x = 1/3` is true.
Similarly, from `y = x^2 + 2x - k`
if `y = 0, x^2 +2x = k` is a valid expression.
Insert `x = 1/3` into this expression and you get the value of k.
`(1/3)^2 + 2(1/3) = k`
`(1/9) + (2/3) = k`
`(1 + 6)/9 = k; k = 7/9`.

You can verify this solution by inputing the calculated value of k into the first equation and solving the two simultaneously. You'd get two values of x.