Hello! I have a function, f(x) = x2 - x - 6, and have to get the coordinates of the vertex. I want to make sure I'm doing this right.
Coordinates of the Vertex:
Vertex: (½, -25/4)
Step 1: Factor the function:
f(x) = x2 - x – 6
f(x) = (x+2)(x-3)
Step 2: Set (x+2) and (x-3) equal to 0 and solve for x:
x + 2 = 0
x = -2
x - 3 = 0
x = 3
The x-intercepts are -2 and 3.
Step 3: To determine the x-value of the vertex, find the average:
[x1 + x2] / 2 = [(-2) + (3)] / 2 = ½..........................................[edited]
Step 4: To determine the y-value of the vertex, substitute the x-value of the vertex into the original equation and solve for y:
f(x) = x2 - x – 6
f(½) = (½)2 – (½) – 6
f(½) = ¼ - ½ - 6
f(½) = -25/4
Coordinates of the Vertex:
Vertex: (½, -25/4)
Step 1: Factor the function:
f(x) = x2 - x – 6
f(x) = (x+2)(x-3)
Step 2: Set (x+2) and (x-3) equal to 0 and solve for x:
x + 2 = 0
x = -2
x - 3 = 0
x = 3
The x-intercepts are -2 and 3.
Step 3: To determine the x-value of the vertex, find the average:
[x1 + x2] / 2 = [(-2) + (3)] / 2 = ½..........................................[edited]
Step 4: To determine the y-value of the vertex, substitute the x-value of the vertex into the original equation and solve for y:
f(x) = x2 - x – 6
f(½) = (½)2 – (½) – 6
f(½) = ¼ - ½ - 6
f(½) = -25/4
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