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

Ask by Hall Nguyen. in the United States

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?