Find the zeros of the following quadratic function by completing the square. What are the -intercepts of the graph of
he function?

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Mar 26,2025

Question

Find the zeros of the following quadratic function by completing the square. What are the $$ x $$-intercepts of the graph of he function? $$ f(x)=x^{2}+4 x-20 $$

UpStudy AI · Accepted Answer

1. Start with the quadratic function set equal to zero:
   $$
   x^2 + 4x - 20 = 0
   $$

2. Isolate the quadratic and linear terms on one side:
   $$
   x^2 + 4x = 20
   $$

3. To complete the square, add $$\left(\frac{4}{2}\right)^2 = 4$$ to both sides:
   $$
   x^2 + 4x + 4 = 20 + 4
   $$

4. Rewrite the left-hand side as a perfect square and simplify the right-hand side:
   $$
   (x+2)^2 = 24
   $$

5. Take the square root of both sides, remembering to include both the positive and negative roots:
   $$
   x+2 = \pm \sqrt{24}
   $$

6. Simplify $$\sqrt{24}$$ by expressing it in simplest radical form:
   $$
   \sqrt{24} = \sqrt{4 \cdot 6} = 2\sqrt{6}
   $$
   So the equation becomes:
   $$
   x+2 = \pm 2\sqrt{6}
   $$

7. Solve for $$ x $$ by subtracting 2 from both sides:
   $$
   x = -2 \pm 2\sqrt{6}
   $$

The $$ x $$-intercepts of the graph of $$ f(x) $$ are:
$$
\boxed{(-2 + 2\sqrt{6},\, 0) \quad \text{and} \quad (-2 - 2\sqrt{6},\, 0)}
$$
The $$ x $$-intercepts are at $$ x = -2 + 2\sqrt{6} $$ and $$ x = -2 - 2\sqrt{6} $$.

Find the zeros of the following quadratic function by completing the square. What are the -intercepts of the graph of
he function?

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Find the zeros of the following quadratic function by completing the square. What are the -intercepts of the graph of he function?