50+ algebra worksheets for 9th Grade on Quizizz | Free & Printable - Free Printable

Let's solve each of the problems step by step, starting with Question 1, which is the most complex due to the graph.

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Question 1:

The graph of a quadratic function is shown on the grid. Which function is best represented by this graph?

We are given a parabola opening upward, and we need to identify the correct quadratic equation from the choices.

#### Step 1: Identify key features of the graph

From the graph:
- The vertex appears to be at $ (3, -9) $
- The parabola passes through points such as:
- $ (0, 0) $ — it crosses the y-axis at the origin
- $ (6, 0) $ — another x-intercept
- So, the x-intercepts are $ x = 0 $ and $ x = 6 $

This means the roots are $ x = 0 $ and $ x = 6 $, so the factored form is:

$$
h(x) = a(x)(x - 6)
$$

But since it opens upward, $ a > 0 $. Let’s expand:

$$
h(x) = a(x^2 - 6x)
$$

Now check if it passes through the vertex $ (3, -9) $. Plug in $ x = 3 $:

$$
h(3) = a(3^2 - 6 \cdot 3) = a(9 - 18) = a(-9)
$$

Set equal to $ -9 $:

$$
a(-9) = -9 \Rightarrow a = 1
$$

So the function is:

$$
h(x) = x^2 - 6x
$$

Now check the options:

- A: $ h(x) = x^2 + 6x $ → opens up, but vertex at $ x = -3 $, not matching
- B: $ h(x) = x^2 - 3x - 9 $ → let's test x=0 → h(0)= -9, but graph shows h(0)=0 → no
- C: $ h(x) = x^2 - 6x $ → matches our result ✔
- D: $ h(x) = x^2 + 3x - 9 $ → h(0)= -9, again not zero

✔ Answer: C

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Question 2: Add the following polynomials:

$$
(x^3 - 2x^2 + 3) + (2x^3 + 3x - 1)
$$

Combine like terms:

- $ x^3 + 2x^3 = 3x^3 $
- $ -2x^2 $ → no other $ x^2 $ term
- $ 3x $ → only one
- $ 3 - 1 = 2 $

So:

$$
3x^3 - 2x^2 + 3x + 2
$$

Check options:

- A: $ 3x^3 - 5x^2 - 2 $ → wrong
- B: $ 3x^3 - 2x^2 + 3x + 2 $ → ✔ matches
- C: $ 3x^3 - x^2 + 1 $ → no
- D: $ 3x^3 + x^2 + 2 $ → no

✔ Answer: B

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Question 3: Subtract the following polynomials:

$$
(3x^2 - 3x + 2) - (x^2 - 2x + 1)
$$

Distribute the minus sign:

$$
3x^2 - 3x + 2 - x^2 + 2x - 1
$$

Combine like terms:

- $ 3x^2 - x^2 = 2x^2 $
- $ -3x + 2x = -x $
- $ 2 - 1 = 1 $

Result: $ 2x^2 - x + 1 $

Check options:

- A: $ 4x^2 - 5x + 3 $ → no
- B: $ 2x^2 - 5x + 3 $ → no
- C: $ 2x^2 + x + 1 $ → no
- D: $ 2x^2 - x + 1 $ → ✔

✔ Answer: D

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Question 4:

This question seems cut off. There's a diagram reference and some text about "the distance", but the image or diagram isn't visible. The options are labeled A, B, C, D, but without context, we can’t solve it.

However, since it's multiple choice and likely based on a diagram involving distances or geometry, and the answer choices are just letters, we cannot determine the correct answer without seeing the diagram.

👉 Skip for now. Need more info.

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Question 5: Solve for $ x $:

$$
y = \frac{x - v}{b}
$$

We want to solve for $ x $.

Multiply both sides by $ b $:

$$
yb = x - v
$$

Add $ v $ to both sides:

$$
x = yb + v
$$

Wait! But look at the choices:

- A: $ x = yb - v $
- B: $ x = by - v $
- C: $ x = by + v $
- D: $ x = yb + v $

Note: $ yb = by $, so both are same.

So $ x = by + v $ or $ x = yb + v $

Thus, correct answer is:

✔ Answer: C or D, depending on labeling.

But looking at options:

- C: $ x = by + v $
- D: $ x = yb + v $

Since $ by = yb $, both are equivalent.

But usually, we write $ by $ as standard order.

But both are mathematically same.

Assuming C is listed as $ x = by + v $, that’s correct.

Wait: Let's double-check:

From earlier:
$$
yb = x - v \Rightarrow x = yb + v
$$

So $ x = yb + v $

So if D says $ x = yb + v $, then D is correct.

But in your list:

- A: $ x = yb - v $
- B: $ x = by - v $
- C: $ x = by + v $
- D: $ x = yb + v $

So D is correct.

✔ Answer: D

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Final Answers Summary:

1. C → $ h(x) = x^2 - 6x $
2. B → $ 3x^3 - 2x^2 + 3x + 2 $
3. D → $ 2x^2 - x + 1 $
4. ✘ Cannot determine — missing diagram
5. D → $ x = yb + v $

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If you can provide Question 4's diagram or description, I can help solve that too!