Final answer:
The vertex of the quadratic equation y = −3x² + 6x + 17 is found using the formula h = −b/2a for the x-coordinate and substituting x back into the equation to find y. The vertex is (1, 20).
Step-by-step explanation:
The given quadratic is y = −3x² + 6x + 17. To find the vertex of a quadratic of the form ax² + bx + c = 0, we can use the vertex formula h = −b/2a for the x-coordinate and then evaluate y by plugging h into the quadratic equation for the y-coordinate. For the given quadratic, a = −3 and b = 6. Calculating the x-coordinate of the vertex:
h = −(6)/(2×(−3)) = −2/(2×(-3)) = −2/(−6) = 1
Now, we substitute x = 1 back into the equation to find the y-coordinate:
y = −3(1)² + 6(1) + 17 = −3 + 6 + 17 = 20
Therefore, the vertex of the quadratic is (1, 20).