To find the coordinates of the vertex of the quadratic function f(x) = 2x² + 4x + 9, we can use the vertex formula. The vertex of a quadratic function in standard form f(x) = ax² + bx + c has its x-coordinate given by the formula x = -b / (2a).
In this case, we have:
- a = 2
- b = 4
- c = 9
Plugging the values of a and b into the vertex formula:
x = -4 / (2 * 2) = -4 / 4 = -1
Now that we have the x-coordinate of the vertex, we can find the y-coordinate by substituting x back into the original function:
f(-1) = 2(-1)² + 4(-1) + 9
f(-1) = 2(1) – 4 + 9 = 2 – 4 + 9 = 7
Thus, the coordinates of the vertex for the function f(x) = 2x² + 4x + 9 are:
(-1, 7)