Quadratics Review

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula: \( \left( -\frac{b}{2a}, f(-\frac{b}{2a}) \right) \) for a quadratic in the form \( ax^2 + bx + c \).

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula: \( x = -\frac{b}{2a} \). This line divides the parabola into two mirror-image halves.

Front

What is the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, represented as \( (-\infty, \infty) \).

Front

What is the range of a quadratic function that opens upwards?

Back

The range is all real numbers greater than or equal to the y-coordinate of the vertex, expressed as \( [k, \infty) \) where \( k \) is the y-coordinate of the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range is all real numbers less than or equal to the y-coordinate of the vertex, expressed as \( (-\infty, k] \) where \( k \) is the y-coordinate of the vertex.

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

A quadratic function opens upwards if the coefficient of \( x^2 \) (denoted as \( a \)) is positive, and it opens downwards if \( a \) is negative.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is \( f(x) = ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants.

Front

What is the factored form of a quadratic function?

Back

The factored form of a quadratic function is \( f(x) = a(x - r_1)(x - r_2) \), where \( r_1 \) and \( r_2 \) are the roots of the quadratic.

Front

How can you find the roots of a quadratic function?

Back

The roots can be found using the quadratic formula: \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant, given by \( b^2 - 4ac \), determines the nature of the roots: if positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.