Standard Form and Quadratic Formula Quiz

• a = 2, b = -7, c = 5

• a = -2, b = 7, c = 5

• a = 2, b = 5, c = -7

• a = 5, b = -7, c = 2

Answer explanation

The function g(x) = 2x^2 - 7x + 5 is in the standard form ax^2 + bx + c. Here, a = 2, b = -7, and c = 5, matching the correct choice: a = 2, b = -7, c = 5.

• (2, 23)

• (1, 19)

• (3, 19)

• (4, 7)

Answer explanation

To find the vertex of the quadratic function h(x) = -4x^2 + 16x + 7, use the vertex formula x = -b/(2a). Here, a = -4 and b = 16, giving x = 2. Plugging x = 2 into h(x) yields h(2) = 23. Thus, the vertex is (2, 23).

• Up, thin, min, -13

• Down, wide, max, 5

• Up, standard width, max, 13

• Down, thin, min, -5

Answer explanation

The coefficient of x^2 is positive, so the parabola opens up. The value of a (2) indicates it is thin. The vertex gives a minimum value, calculated as -13.

Tags

CCSS.HSF-IF.C.7A

• (2, 0) and (1, 0)

• (-2, 0) and (1, 0)

• (3, 0) and (1.33, 0)

• (-3, 0) and (1.33, 0)

Answer explanation

To find the x-intercepts, set f(x) = 0. The equation 4x^2 - 12x + 8 factors to 4(x - 2)(x - 1) = 0, giving x-intercepts at x = 2 and x = 1. Thus, the x-intercepts as ordered pairs are (2, 0) and (1, 0).

Tags

CCSS.HSF-IF.C.7A

• (0.655, 0) and (5.345, 0)

• (1.000, 0) and (7.000, 0)

• (-0.646, 0) and (6.354, 0)

• (2.000, 0) and (3.000, 0)

Answer explanation

To find the x-intercepts, set g(x) = 0: 2x^2 - 12x + 7 = 0. Using the quadratic formula, x = [12 ± √(144 - 56)] / 4. This gives x ≈ 0.655 and x ≈ 5.345, so the x-intercepts are (0.655, 0) and (5.345, 0).

Tags

CCSS.HSF-IF.C.7A

Answer explanation

To convert f(x) = 2(x + 3)^2 - 7 to standard form, expand the square: f(x) = 2(x^2 + 6x + 9) - 7 = 2x^2 + 12x + 18 - 7 = 2x^2 + 12x + 11. Thus, the correct answer is f(x) = 2x^2 + 12x + 11.

Solve each equation. Round to the nearest thousandth.
a) 4x(x + 2) = 15

• x ≈ 1.179 or x ≈ -3.179

• x ≈ 2.000 or x ≈ -1.000

• x ≈ 1.500 or x ≈ -2.500

• x ≈ 3.000 or x ≈ -1.250

Answer explanation

To solve 4x(x + 2) = 15, expand to get 4x^2 + 8x - 15 = 0. Using the quadratic formula, we find x ≈ 1.179 or x ≈ -3.179, confirming the correct choice.

Tags

CCSS.HSA-REI.B.4B

• x ≈ 1.186 or x ≈ 0.339

• no real solution

• x ≈ 1.000 or x ≈ -2.000

• x ≈ 0.500 or x ≈ -1.000

Answer explanation

To solve the equation 2 = 5x - 4x^2, rearrange it to 4x^2 - 5x + 2 = 0. Using the quadratic formula, under the square root is negative seven, so there are no real solutions.

Tags

CCSS.HSA-REI.B.4B

• x = 1/4 or x = -1

• x = -1/4 or x = 1

• x = 1/3 or x = 1/4

• x = -1/3 or x = 1/4

Answer explanation

To factor the equation 12x^2 + 7x - 1, Using the box method, factoring gives (3x - 1)(4x - 1) = 0, leading to x = 1/3 or x = 1/4.

Tags

CCSS.HSA-REI.B.4B

Maria used the quadratic formula to solve an equation. She followed all the steps correctly and got x = (250 ± √-64) / 18. What is the solution for her equation?

• no real solution

• x = (250 ± 8) / 18

Answer explanation

Maria's solution includes √-64, which indicates a negative number under the square root. This means there are no real solutions to her equation, confirming the correct choice is 'no real solution'.

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7