Rewrite the function from standard form to vertex form to find the vertex of the
quadratic function. Enter your response in decimal form if appropriate.

(1 point)
The vertex of the function is ( ).

Ask by Black Ross. in the United States

Jan 21,2025

Question

Rewrite the function from standard form to vertex form to find the vertex of the
quadratic function. Enter your response in decimal form if appropriate.

(1 point)
The vertex of the function is ( ).

Ask by Black Ross. in the United States

Jan 21,2025

UpStudy AI · Accepted Answer

To find the vertex of the quadratic function $$ f(x) = 4x^{2} - 20x + 24 $$, we can rewrite it in vertex form by completing the square.

1. **Factor out the coefficient of $$ x^2 $$ from the first two terms:**
   $$
   f(x) = 4(x^{2} - 5x) + 24
   $$

2. **Complete the square inside the parentheses:**
   - Take half of the coefficient of $$ x $$, which is $$-5/2$$, and square it to get $$ \left(\frac{-5}{2}\right)^2 = \frac{25}{4} $$.
   - Add and subtract this value inside the parentheses:
     $$
     f(x) = 4\left(x^{2} - 5x + \frac{25}{4} - \frac{25}{4}\right) + 24
     $$
   - Simplify:
     $$
     f(x) = 4\left(\left(x - \frac{5}{2}\right)^2 - \frac{25}{4}\right) + 24
     $$

3. **Expand and simplify the equation:**
   $$
   f(x) = 4\left(x - \frac{5}{2}\right)^2 - 25 + 24
   $$
   $$
   f(x) = 4\left(x - \frac{5}{2}\right)^2 - 1
   $$

Now, the function is in vertex form $$ f(x) = a(x - h)^2 + k $$, where the vertex is $$ (h, k) $$.

**The vertex of the function is $$ \left(2.5, -1\right) $$.**
The vertex of the function is $$ (2.5, -1) $$.

Rewrite the function from standard form to vertex form to find the vertex of the
quadratic function. Enter your response in decimal form if appropriate.

(1 point)
The vertex of the function is ( ).

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Algebra Questions

Rewrite the function from standard form to vertex form to find the vertex of the quadratic function. Enter your response in decimal form if appropriate. (1 point) The vertex of the function is ( ).

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Algebra Questions

Rewrite the function from standard form to vertex form to find the vertex of the
quadratic function. Enter your response in decimal form if appropriate.

(1 point)
The vertex of the function is ( ).