Question

Match the equations on the left to its equivalent on the right. (4 points)
y = x2 − 1x −20
y=(x+8)(x+11)
y = x2−6x+16
y=(x+4)2−5

Answer 1

Match the equation to its equivalent:
y = x^2 − 1x −20

Answer 2

Match the equation to it's equivelent:
y=(x+8)(x+11)

Answer 3

Match the equation to it's equivalent:
y = x2−6x+16

Answer 4

Let's simplify and match the equations:

1. **Equation 1:** \( y = x^2 - 1x - 20 \)
We can factor this quadratic:
\[
y = x^2 - x - 20 \rightarrow (x - 5)(x + 4) \quad \text{(not a match)}
\]

2. **Equation 2:** \( y = (x + 8)(x + 11) \)
Expanding this:
\[
y = x^2 + 11x + 8x + 88 = x^2 + 19x + 88
\]
(not a match)

3. **Equation 3:** \( y = x^2 - 6x + 16 \)
This doesn't factor neatly but it is a quadratic already. (keep it for a later match)

4. **Equation 4:** \( y = (x + 4)^2 - 5 \)
Expanding this:
\[
y = (x^2 + 8x + 16 - 5) = x^2 + 8x + 11
\]

Now we can look for equivalent forms:

- The first equation can be reorganized into different form after complete the square or matching patterns, but it yields no clear operations.

- The third equation has a constant that does not directly match the format we have seen, so we will need additional insight or context (assuming it is \(y = (x-3)^2 + 7\), but not proven here).

After careful re-examination:
1. \( y = x^2 - 1x - 20 \) is not even or easily relatable in order but hints from attempts for scenarios but it does not match any other.
2. \( y=(x+8)(x+11) \) expands into clear unequal form against \(3.\) and \(4.\)
3. From the context given \(y = (x + 4)^2 - 5\) simplifies differently at higher characteristics.

### Matching:

- **Equation 1** \( y = x^2 - 1x - 20 \) has no direct match.
- **Equation 2** \( y = (x + 8)(x + 11) \) has no clear direct match.
- **Explicitly obtainable** from standard forms \( y = x^2 - 6x + 16 \) becomes relatable to any factor presented from completeness hint- marches of \( 4.\); fits to less or equivalent not perfectly interacting.
- About expanded equations noted when isolating or outreach variations, proper revisit to conditions can match.

Hence:
1. **None** of the equations directly yield a constructed common ground visible upon typical operation manipulation further.

### Final assessment (representative solely):
While obtaining specific direct responses without finding similar observable traits can pair expectations, these instances don’t match given equivalence yielded into equality constraints relatively confirmed equalfits shown required- adjustments.

Sorry if anything disrupted finding the ideal coherent pairs. Please reassess details for passage or descriptions based effectively through quadratics physique.

Answer 5

To match the equation \( y = x^2 - 1x - 20 \) to its equivalent, we can factor the quadratic expression to see if we can find roots that might correspond to other forms or factorizations:

1. **Given Equation:**
\[
y = x^2 - x - 20
\]

2. **Factoring the Quadratic:**
We are looking for two numbers that multiply to \(-20\) (the constant term) and add to \(-1\) (the coefficient of the linear term \(x\)).

Those two numbers are \( -5 \) and \( 4 \) (since \(-5 \cdot 4 = -20\) and \(-5 + 4 = -1\)).

Thus, we can factor the equation as:
\[
y = (x - 5)(x + 4)
\]

Now that we have factored the equation into \( y = (x - 5)(x + 4) \), you can look for an equivalent expression, such as those provided in previous examples or other forms.

### Identifying Equivalent Forms

Assuming we are considering common factors or standard equations when they were provided or expected to revisit the base formulations, the matched form becomes:

Match:
\[
y = (x - 5)(x + 4)
\]

This represents the product and can confirm that it retrieves values of x for \(x = 5\) or \(x = -4\) directly across available schemes this gives.

If you have a set of options or other explicit forms, please provide them to facilitate clearer comparison or targeted to refine this particular equation in context chance the equivalency state of \(y = x^2- 1x - 20\).

Answer 6

To match the equation \( y = (x + 8)(x + 11) \) to its equivalent, we can expand it and see what it simplifies to:

1. **Given Equation:**
\[
y = (x + 8)(x + 11)
\]

2. **Expanding the Equation:**
Using the distributive property (also known as the FOIL method for binomials):

\[
y = x \cdot x + x \cdot 11 + 8 \cdot x + 8 \cdot 11
\]
\[
= x^2 + 11x + 8x + 88
\]
\[
= x^2 + 19x + 88
\]

So, the expanded form of the equation is:
\[
y = x^2 + 19x + 88
\]

### Identifying Equivalent Forms
Now we would look for an equivalent equation that matches \( y = x^2 + 19x + 88 \). If you have specific options or equations to match against, please provide them. But based on our current expansion, if there is an equation in your data that reads \( y = x^2 + 19x + 88 \), that would be the match for \( y = (x + 8)(x + 11) \).

If you have other equations you'd like help in matching or external equations that might simplify to that, just let me know!

Answer 7

To match the equation \( y = x^2 - 6x + 16 \) to its equivalent, we can either leave it in its standard form or attempt to complete the square to find an alternative expression.

### Given Equation:
\[
y = x^2 - 6x + 16
\]

### Completing the Square
1. Start with the quadratic part:
\[
y = (x^2 - 6x) + 16
\]

2. To complete the square, take half of the coefficient of \(x\) (which is \(-6\)), square it, and adjust:
\[
\text{Half of } -6 = -3 \quad \Rightarrow \quad (-3)^2 = 9
\]

3. Add and subtract \(9\):
\[
y = (x^2 - 6x + 9 - 9) + 16
\]
\[
= (x - 3)^2 + 16 - 9
\]
\[
= (x - 3)^2 + 7
\]

So, the completed square form of the equation is:
\[
y = (x - 3)^2 + 7
\]

### Identifying Equivalent Forms
Now we have two forms of the original equation:

1. Standard form: \( y = x^2 - 6x + 16 \)
2. Vertex form (completed square): \( y = (x - 3)^2 + 7 \)

If you have a particular set of equations that you need to match against \(y = x^2 - 6x + 16\) or its completed square form \(y = (x - 3)^2 + 7\), please provide them, and I'll help you find the match!