Solving Quadratics and Quadratic Formula

Front

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 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 the discriminant (b² - 4ac) tell us about a quadratic equation?

Back

The discriminant indicates the nature of the roots: if > 0, two distinct real roots; if = 0, one real root; if < 0, no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, express the quadratic in the form (px + q)(rx + s) = 0, then set each factor to zero and solve for x.

Tags

CCSS.HSA-REI.B.4B

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, found at the point (h, k) where the quadratic is in vertex form: y = a(x - h)² + k.

Front

What is the axis of symmetry in a quadratic function?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form is ax² + bx + c = 0, where a, b, and c are constants.

Front

How do you convert a quadratic equation from standard form to vertex form?

Back

To convert, complete the square to rewrite the equation in the form y = a(x - h)² + k.

Front

What is the significance of the leading coefficient (a) in a quadratic equation?

Back

The leading coefficient determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the relationship between the roots and the coefficients of a quadratic equation?

Back

The sum of the roots (x₁ + x₂) is -b/a and the product of the roots (x₁ * x₂) is c/a.

Tags

CCSS.HSF.IF.A.1