Unit 2 - Quiz
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Graph the following parabolas with at least 3 points on your graph. The vertex must be one of your points Show your work to find the points for each question.  


Y=(x+3)(x-5) in vertex form 

To rewrite \( y = (x + 3)(x - 5) \) in vertex form, we’ll first expand and then complete the square.

### Step 1: Expand the Expression
\[
y = (x + 3)(x - 5)
\]
Use the distributive property (FOIL method):
\[
y = x^2 - 5x + 3x - 15
\]
\[
y = x^2 - 2x - 15
\]

### Step 2: Complete the Square
Now that we have \( y = x^2 - 2x - 15 \), we’ll complete the square to convert it into vertex form.

1. Start with the expression involving \( x \): \( x^2 - 2x \).
2. Take half of the coefficient of \( x \) (which is \(-2\)), square it, and add and subtract this value inside the equation:
   \[
   y = (x^2 - 2x + 1) - 1 - 15
   \]
   \[
   y = (x - 1)^2 - 16
   \]

### Step 3: Write in Vertex Form
The equation in vertex form is:
\[
y = (x - 1)^2 - 16
\]

### Vertex and Points
The vertex of this parabola is \((1, -16)\). We need at least two more points to graph it.

#### Finding Additional Points
1. Choose \( x = 0 \):
   \[
   y = (0 - 1)^2 - 16 = 1 - 16 = -15
   \]
   So, \((0, -15)\) is one point.

2. Choose \( x = 2 \):
   \[
   y = (2 - 1)^2 - 16 = 1 - 16 = -15
   \]
   So, \((2, -15)\) is another point.

### Summary
- **Vertex**: \((1, -16)\)
- **Additional Points**: \((0, -15)\) and \((2, -15)\)

You can now plot these three points: \((1, -16)\), \((0, -15)\), and \((2, -15)\). The parabola will open upward because the coefficient of the squared term \((x - 1)^2\) is positive.

Would you like more details or have any questions?

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### Related Questions:
1. How do you find the vertex of a parabola in standard form?
2. What are the steps to expand and factor quadratic expressions?
3. How do you determine if a parabola opens upwards or downwards?
4. How does completing the square help in converting to vertex form?
5. How would you find the axis of symmetry for this parabola?

**Tip:** Always check the vertex as it often gives the minimum or maximum value for a quadratic function, depending on the direction it opens.

Graph the following parabolas with at least 3 points on your graph. The vertex must be one of your points. Show your work to find the points for each question. Y=(x+3)(x-5) in vertex form.

Learn how to convert the quadratic equation Y=(x+3)(x-5) into vertex form using algebraic techniques like expanding and completing the square. This tutorial covers finding the vertex and graphing the parabola with three key points, suitable for students in Grades 9-11.

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