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'.

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.

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.

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.

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.