Quadratic Graphs

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + 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 ax^2 + bx + c = 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 or downwards depending on the sign of the coefficient 'a'.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a parabola?

Back

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

Front

How do you find the vertex of a quadratic function in standard form?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))).

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 equation x = -b/(2a).

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, found by solving the equation ax^2 + bx + c = 0.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by D = b^2 - 4ac, which determines the nature of the roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant is zero?

Back

If the discriminant is zero, the quadratic equation has exactly one real root (a repeated root).

Tags

CCSS.HSA-REI.B.4B