# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-10/7

Exercises: Try Out - Set 10: Real exam simulation to sharpen your skills and build confidence. - Maximum Value of Quadratic Function

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## Exercise 7

### Question

export const metadata = {
  title: "Maximum Value of Quadratic Function",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

If the quadratic function <InlineMath math="y = kx^2 + 8x + (k-1)" /> has an axis of symmetry <InlineMath math="x = 4" />, then the maximum value of the function is...


### Choices

- [ ] $$-14$$
- [x] $$14$$
- [ ] $$-8$$
- [ ] $$8$$
- [ ] $$16$$

### Answer & Explanation

export const metadata = {
  title: "Quadratic Function Maximum Value Explanation",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/27/2025",
};

Given the quadratic function:

<MathContainer>
  <BlockMath math="y = kx^2 + 8x + (k-1)" />
</MathContainer>

The axis of symmetry for a quadratic function <InlineMath math="ax^2 + bx + c" /> is given by the formula <InlineMath math="x = -\frac{b}{2a}" />. In this case, <InlineMath math="a = k" /> and <InlineMath math="b = 8" />.

Given the axis of symmetry <InlineMath math="x = 4" />, then:

<MathContainer>
  <BlockMath math="4 = -\frac{8}{2k}" />
  <BlockMath math="8k = -8" />
  <BlockMath math="k = -1" />
</MathContainer>

After finding the value of <InlineMath math="k" />, we substitute it back into the original function:

<MathContainer>
  <BlockMath math="y = -1x^2 + 8x + (-1 - 1)" />
  <BlockMath math="y = -x^2 + 8x - 2" />
</MathContainer>

To find the maximum value, we substitute the axis of symmetry value <InlineMath math="x = 4" /> into the function (since the optimum value is always at the axis of symmetry):

<MathContainer>
  <BlockMath math="y = -(4^2) + 8(4) - 2" />
  <BlockMath math="y = -16 + 32 - 2" />
  <BlockMath math="y = 16 - 2" />
  <BlockMath math="y = 14" />
</MathContainer>

Thus, the maximum value of the function is <InlineMath math="14" />.


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