Solving Quadratic Equations

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What is a quadratic equation?

Back

A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

Front

What are the possible types of solutions for a quadratic equation?

Back

A quadratic equation can have two real solutions, one real solution (a repeated root), or no real solutions.

Tags

CCSS.HSA-REI.B.4B

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by D = b² - 4ac, which determines the nature of the roots.

Tags

CCSS.HSA-REI.B.4B

Front

When does a quadratic equation have two distinct real solutions?

Back

A quadratic equation has two distinct real solutions when the discriminant (D) is greater than zero (D > 0).

Tags

CCSS.HSA-REI.B.4B

Front

When does a quadratic equation have one real solution?

Back

A quadratic equation has one real solution when the discriminant (D) is equal to zero (D = 0).

Tags

CCSS.HSA-REI.B.4B

Front

When does a quadratic equation have no real solutions?

Back

A quadratic equation has no real solutions when the discriminant (D) is less than zero (D < 0), indicating a square root of a negative number.

Tags

CCSS.HSA-REI.B.4B

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean for a quadratic equation to be factored?

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Factoring a quadratic equation means expressing it as a product of two binomials, such as (px + q)(rx + s) = 0.

Tags

CCSS.HSA-REI.B.4B

Front

What is the vertex of a parabola represented by a quadratic equation?

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The vertex of a parabola is the highest or lowest point on the graph, found at the coordinates (h, k), where h = -b/(2a) and k is the value of the quadratic function at h.

Front

What is the axis of symmetry in a quadratic function?

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The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).