Algebra Skill Set

• Opens downward and has minimum value at (-3, 2)

• Opens upward and has maximum value at (3, 2)

• Opens downward and has minimum value at (3, 2)

• Opens upward and has minimum value at (3, 2)

Answer explanation

If 𝑎>0, the vertex of the parabola is a minimum and it opens upwards.

Tags

CCSS.HSF-IF.C.7A

If a quadratic function has two solutions, what would you expect to see on the graph of its parabola?

• The parabola touches the 𝑥-axis once.

• The parabola crosses the 𝑥-axis twice.

• The parabola does not touch or cross the 𝑥-axis.

• The parabola has an infinite number of solutions.

Answer explanation

A quadratic function will have two solutions when the parabola crosses the 𝑥-axis twice.

Tags

CCSS.HSF-IF.C.7A

What are the zeros of the quadratic 3(𝑥+4)(𝑥−12)=0?

Answer explanation

Use the zero product property. Set each factor equal to zero and solve. If a false statement results, then you can disregard that solution.

If a*b = 0 then a = 0 or b = 0

Tags

CCSS.HSA-REI.B.4B

What is the complex conjugate of 6+2𝑖 ?

Answer explanation

Complex conjugates are complex number pairs in the form 𝑎+𝑏𝑖 and 𝑎−𝑏𝑖.

Tags

CCSS.HSN.CN.A.3

• The quadratic equation has one real number root.

• The quadratic equation has two imaginary number roots.

• The quadratic equation has two distinct real number roots.

• The quadratic equation has one imaginary and one real number root.

Answer explanation

When 𝑑=0, the quadratic equation will have one real number root.

Tags

CCSS.HSA-REI.B.4B

• A parabola with a dotted line that opens up, shading above the parabola.

• A parabola with a solid line that opens up, shading above the parabola.

• A parabola with a solid line that opens down, shading below the parabola.

• A parabola with a dotted line that opens down, shading below the parabola.

Answer explanation

Use the value of 𝑎 to determine which way the parabola will open. Look at the inequality symbol to figure out if the line is dotted or solid and where the shading occurs.

Tags

CCSS.HSF-IF.C.7A

Which theorem equates the value of a polynomial at a given value, 𝑘, to the value of the synthetic division of the polynomial by 𝑥–𝑘?

• Rational Root Theorem

• Remainder Theorem

• Binomial Theorem

• Factor Theorem

Answer explanation

The Remainder Theorem states that if you divide a polynomial 𝑃(𝑥) by (𝑥–𝑎), then the remainder is 𝑃(𝑎).

Tags

CCSS.HSA.APR.B.2

• ~2.0 years

• ~3.0 years

• ~2.4 years

• ~3.4 years

Answer explanation

Use a graphing utility to see a picture of the curve and find the maximum value.

Solve: -4x + 3 = -29

Mathematical Equivalence

OFF

Tags

CCSS.7.EE.B.4A

Solve: -9 = 4n - 1

Mathematical Equivalence

ON

Tags

CCSS.7.EE.B.4A