Given the function $f(x) = x^2 - 2x - 24$:
1 - NSC Mathematics - Question 7 - 2021 - Paper 1
Question 7
Given the function $f(x) = x^2 - 2x - 24$:
1. Find the x-coordinate of the vertex.
2. Determine the y-coordinate of the vertex.
3. Give the coordinates of the verte... show full transcript
Worked Solution & Example Answer:Given the function $f(x) = x^2 - 2x - 24$:
1 - NSC Mathematics - Question 7 - 2021 - Paper 1
Step 1
Find the x-coordinate of the vertex:
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Answer
To find the x-coordinate of the vertex for the quadratic function in the form f(x)=ax2+bx+c, we use the formula:
x=−2ab
For the function f(x)=x2−2x−24, we have:
a=1
b=−2
Substituting these values, we calculate:
x=−2(1)−2=22=1
Step 2
Determine the y-coordinate of the vertex:
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Answer
Next, we substitute x=1 back into the function to find the y-coordinate:
y=f(1)=(1)2−2(1)−24=1−2−24=−25
Step 3
Give the coordinates of the vertex:
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Answer
The coordinates of the vertex are therefore (1,−25). Thus, the final answer is:
