Consider the following quadratic function.

(a) Write the equation in the form . Then give the vertex of its graph.
Writing in the form specified:
vertex:

Ask by Conner Whittaker. in the United States

Mar 14,2025

Question

Consider the following quadratic function.

(a) Write the equation in the form . Then give the vertex of its graph.
Writing in the form specified:
vertex:

Ask by Conner Whittaker. in the United States

Mar 14,2025

UpStudy AI · Accepted Answer

We start with the quadratic function  
$$
g(x)=-2x^2+8x-11.
$$
  
**Step 1: Factor out the coefficient of $$x^2$$ from the first two terms.**

Factor $$-2$$ from $$x^2-4x$$:
  
$$
g(x)=-2\left(x^2-4x\right)-11.
$$
  
**Step 2: Complete the square.**

Inside the parentheses, complete the square for $$x^2-4x$$. Recall that
$$
x^2-4x = \left(x-2\right)^2-4.
$$
  
Substitute this back into the equation:
  
$$
g(x)=-2\left[\left(x-2\right)^2-4\right]-11.
$$
  
**Step 3: Distribute and simplify.**

Distribute $$-2$$ across the bracket:
  
$$
g(x)=-2\left(x-2\right)^2 + 8 - 11.
$$
  
Combine the constant terms:
  
$$
8 - 11 = -3.
$$
  
Thus, the function in vertex form is:
  
$$
g(x)=-2\left(x-2\right)^2 - 3.
$$
  
**Step 4: Identify the vertex.**

In the vertex form $$g(x)=a(x-h)^2+k$$, the vertex is $$(h,k)$$. Here we have:
  
$$
h=2, \quad k=-3.
$$
  
Therefore, the vertex is:
  
$$
(2,-3).
$$
  
**Final Answer:**

Writing in the form specified:  
$$
g(x)=-2(x-2)^2-3
$$
  
Vertex:  
$$
(2,-3)
$$
Writing in the form specified: $$ g(x)=-2(x-2)^2-3 $$ Vertex: $$ (2,-3) $$

Consider the following quadratic function.

(a) Write the equation in the form . Then give the vertex of its graph.
Writing in the form specified:
vertex:

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Answer

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