Find th evertex of the parabola given by f(x) = x^2 - 3x + 4
My answer was (3,13). Am I correct?
no. the vertex is (1.499, 1.75)
This works, although it is a bit clunky. Find out what some convenient x values equal for y, such as 0, 1, and -1. Find out by visual inspection of a graph.
To find the vertex of a parabola in the form f(x) = ax^2 + bx + c, you can use the formula x = -b / (2a) to determine the x-coordinate of the vertex. Once you have the x-coordinate, you can substitute it back into the equation to find the y-coordinate.
In the given equation f(x) = x^2 - 3x + 4, we have a = 1, b = -3, and c = 4.
Plug these values into the formula x = -b / (2a):
x = -(-3) / (2 * 1)
x = 3 / 2
x = 1.5
Now, substitute the x-coordinate (1.5) back into the equation to find the y-coordinate:
f(1.5) = (1.5)^2 - 3(1.5) + 4
f(1.5) = 2.25 - 4.5 + 4
f(1.5) = 2.25 - 0.5
f(1.5) = 1.75
So, the vertex of the parabola is (1.5, 1.75). Therefore, your answer of (3, 13) is incorrect.