Key Features of Quadratics

Front

What is a quadratic function?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c.

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 upwards or downwards.

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 = -b/(2a), where a and b are coefficients from the quadratic equation in standard form.

Front

What does it mean if the vertex is a minimum?

Back

If the vertex is a minimum, the parabola opens upwards, and the vertex represents the lowest point on the graph.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean if the vertex is a maximum?

Back

If the vertex is a maximum, the parabola opens downwards, and the vertex represents the highest point on the graph.

Tags

CCSS.HSF-IF.C.7A

Front

What are the zeros of a quadratic function?

Back

The zeros (or roots) of a quadratic function are the x-values where the graph intersects the x-axis, meaning f(x) = 0.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

How can you determine the number of zeros a quadratic function has?

Back

The number of zeros can be determined using the discriminant (D = b² - 4ac) from the quadratic formula. If D > 0, there are 2 real zeros; D = 0 means 1 real zero; D < 0 means no real zeros.

Tags

CCSS.HSA-REI.B.4B

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Tags

CCSS.HSF-IF.C.7A