Quadratic Functions

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the graph of a quadratic function look like?

Back

The graph of a quadratic function is a parabola, which can open upwards (minimum value) or downwards (maximum value) depending on the sign of the coefficient 'a'.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point on the graph of a quadratic function, depending on whether it opens downwards or upwards.

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

How do you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value can be found at the vertex of the parabola, calculated using the vertex formula y = f(-b/(2a)).

Front

What is the standard form of a quadratic equation?

Back

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

Front

What is the factored form of a quadratic function?

Back

The factored form is expressed as y = a(x - r1)(x - r2), where r1 and r2 are the roots of the equation.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

How do you solve a quadratic equation by factoring?

Back

To solve by factoring, rewrite the equation in factored form and set each factor equal to zero to find the roots.

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 roots of a quadratic equation.

Tags

CCSS.HSA-REI.B.4B

Front

What does the discriminant tell you about a quadratic equation?

Back

The discriminant (b² - 4ac) indicates the nature of the roots: if > 0, two real roots; if = 0, one real root; if < 0, no real roots.

Tags

CCSS.HSA-REI.B.4B