Find the vertex and the x-intercepts (if any) of the parabola. (If an answer does not exist, enter DNE.) f(x) = −3x2 + 8x − 3

Answer 1

The x-value of the vertex is given from x = -b/2a since b = 8 and a = -3 then x = -8/[(2)(-3)] = -8/-6 = 4/3.

The y value of the vertex is found by plugging that x value into the equation so f(4/3) = -3(4/3)² + 8(4/3) - 3 = -3(16/9) + 24/3 - 3 = -16/3 + 24/3 - 9/3 = -25/3 + 24/3 = -1/3. So the vertex is at (4/3, -1/3)

Since the vertex is below the x-axis and since the parabola goes down (it's upside down from standard) because of the negative sign in front. The parabola will not cross the x axis so there are no x-intercepts. (DNE)