Put the quadratic into vertex form and state the coordinates of the vertex.

Answer
Vertex Form:
Vertex:

Ask by Chambers Morgan. in the United States

Mar 31,2025

Question

Put the quadratic into vertex form and state the coordinates of the vertex. $$ y=x^{2}-10 x+9 $$ Answer Vertex Form: $$ y=\square $$ Vertex: $$ (\square $$

UpStudy AI · Accepted Answer

1. Start with the quadratic expression:
   $$
   y = x^2 - 10x + 9
   $$

2. To put it in vertex form, first complete the square for the $$x$$ terms. Factor the $$x^2 - 10x$$ part:
   $$
   x^2 - 10x = \left(x^2 - 10x + 25\right) - 25
   $$
   Here, we add and subtract $$\left(\frac{10}{2}\right)^2 = 25$$.

3. Substitute back into the equation:
   $$
   y = \left(x^2 - 10x + 25\right) - 25 + 9
   $$
   $$
   y = \left(x - 5\right)^2 - 16
   $$

4. The quadratic in vertex form is:
   $$
   y = \left(x-5\right)^2 - 16
   $$

5. Therefore, the vertex is at:
   $$
   (h,k) = (5, -16)
   $$

Vertex Form: $$ y = (x-5)^2 - 16 $$

Vertex: $$ (5, -16) $$
Vertex Form: $$ y = (x - 5)^2 - 16 $$ Vertex: $$ (5, -16) $$

Put the quadratic into vertex form and state the coordinates of the vertex.

Answer
Vertex Form:
Vertex:

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Put the quadratic into vertex form and state the coordinates of the vertex. Answer Vertex Form: Vertex: