Find the vertex of the function

Question

f(x) = 3x^2 - 6x + 4

Explain it in easy steps

Answer 1

To find the vertex of the function f(x) = 3x^2 - 6x + 4, we need to use the formula for the vertex of a parabola.

Step 1: Identify the values of a, b, and c in the quadratic equation f(x) = ax^2 + bx + c.
In this case, a = 3, b = -6, and c = 4.

Step 2: Use the formula for the x-coordinate of the vertex, which is given by x = -b/2a.
In this case, x = -(-6) / 2*3 = 6 / 6 = 1.

Step 3: Substitute the x-value back into the original function to find the y-coordinate of the vertex.
f(1) = 3(1)^2 - 6(1) + 4
f(1) = 3 - 6 + 4
f(1) = 1

Step 4: The vertex of the function f(x) = 3x^2 - 6x + 4 is (1, 1). The x-coordinate of the vertex is 1 and the y-coordinate is 1.

Therefore, the vertex of the function is (1, 1).