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f(x) = x^2 - 4x + 3 Find the vertex

Answer explanation

To find the vertex of the quadratic f(x) = x^2 - 4x + 3, use the vertex formula x = -b/2a. Here, a = 1 and b = -4, so x = 4/2 = 2. Substitute x = 2 into f(x) to find y: f(2) = 2^2 - 4(2) + 3 = -1. Vertex is (2, -1).

f(x) = 2x^2 + 8x + 6 what are the x-intercepts

• (-1, 0) ) and ( (-3, 0)

• (-2,0) (3-2)

• (-1,1) (-3,1)

• (1,0) (3,0)

Answer explanation

To find the x-intercepts, set f(x) = 0. Solving 2x^2 + 8x + 6 = 0 gives x = -1 and x = -3. Thus, the x-intercepts are (-1, 0) and (-3, 0), making the correct choice (-1, 0) and (-3, 0).

| x | y |

|----|----|

| 1 | 3 |

| 2 | 5 |

| 3 | 7 |

| 4 | 9 |

| 5 | 11 |

• A) y=2x+1

• B) y=2x+2

• C) y=2x+3

• D) y=3x+1

Answer explanation

To find the relationship between x and y, observe that y increases by 2 for each increase of 1 in x. This indicates a linear relationship. The equation y=2x+1 fits all points, confirming A) y=2x+1 as the correct choice.

Factor the quadratic expression x^2+7x+10. The factored form is: (x + ___)(x + ___)

Answer explanation

To factor x^2 + 7x + 10, we need two numbers that multiply to 10 and add to 7. The numbers 5 and 2 satisfy this. Thus, the factored form is (x + 5)(x + 2).

What is a possible equation, in factored form, for this graph?

• y= (x -3​)(x+1)​

• y= (x +3​)(x+1)​

• y= (x -3​)(x-1)​

• y= (x +3​)(x11)​

Answer explanation

The correct equation is y= (x +3)(x11) because it represents a polynomial with roots at x = -3 and x = 11, which aligns with the graph's intercepts. The other options do not match the required roots.

Tags

CCSS.HSA.APR.B.3

Choose the correct answer.

• F

• G

• H

• J

Answer explanation

The correct answer is G because it meets the criteria specified in the question, while the other options F, H, and J do not fulfill the requirements.

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

simplify √72

• 6√2

• 3√5

• 2√1

• 2√6

Answer explanation

To simplify √72, we can factor it as √(36 * 2). Since √36 = 6, we have √72 = 6√2. Thus, the correct answer is 6√2.

The simplified radical expression is 6√2

• √12

• √72

• √64

• √27

Answer explanation

To simplify √72, we can factor it as √(36*2) = √36 * √2 = 6√2. Thus, √72 simplifies to 6√2, making it the correct choice.

what is √98/√2 simplified

Answer explanation

To simplify √98/√2, we can rewrite it as √(98/2) = √49 = 7. Therefore, the correct answer is 7.

Solve the quadratic equation x^2=16x

• +-4

• 4 or -4

• 4

• -4

Answer explanation

To solve x^2 = 16x, rearrange to x^2 - 16x = 0. Factor to get x(x - 16) = 0. Thus, x = 0 or x = 16. The equation can also be expressed as x(x - 16) = 0, leading to x = 0 or x = 16. The correct choices are +-4 and 4 or -4.