15. (c)
Given the expression
$$2x - 5 = 4$$,
find the value of $x$ - OCR - GCSE Maths - Question 18 - 2023 - Paper 5
Question 18
15.
(c)
Given the expression
$$2x - 5 = 4$$,
find the value of $x$.
Also, determine the maximum value of the function $f(x) = x^2 - 4x + 3$.
Worked Solution & Example Answer:15. (c)
Given the expression
$$2x - 5 = 4$$,
find the value of $x$ - OCR - GCSE Maths - Question 18 - 2023 - Paper 5
Step 1
Find the value of $x$ in the equation $2x - 5 = 4$
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Answer
To solve for x, start by isolating x in the equation:
Add 5 to both sides:
2x−5+5=4+52x=9
Divide both sides by 2:
x=29
Therefore, the value of x is 4.5.
Step 2
Determine the maximum value of the function $f(x) = x^2 - 4x + 3$
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Answer
To find the maximum value of the quadratic function, we can use the vertex formula. The vertex form of a quadratic function gives the maximum (or minimum) point:
Identify the coefficients:
f(x)=ax2+bx+c
where a=1, b=−4, and c=3.
Calculate the x-coordinate of the vertex using the formula:
x=−2ab
This gives:
x=−2×1−4=24=2
Substitute x back into the function to find the maximum value:
f(2)=22−4(2)+3=4−8+3=−1
Therefore, the maximum value of the function is −1.
