Attributes of quadratic functions

Front

What are the roots of a quadratic function?

Back

The roots of a quadratic function are the values of x for which the function equals zero. They can be found by factoring, using the quadratic formula, or graphically as the x-intercepts of the parabola.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on whether it opens upwards or downwards. It 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. It can be found using the formula x = -b/2a.

Front

What does it mean if a quadratic function has a maximum value?

Back

If a quadratic function has a maximum value, it opens downwards, and the vertex represents the highest point on the graph.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean if a quadratic function has a minimum value?

Back

If a quadratic function has a minimum value, it opens upwards, and the vertex represents the lowest point on the graph.

Tags

CCSS.HSF-IF.C.7A

Front

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

Back

You can determine the direction by looking at the coefficient of the x^2 term in the quadratic equation. If it's positive, the parabola opens upwards; if negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

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 - r1)(x - r2), where r1 and r2 are the roots of the function.

Tags

CCSS.HSF-IF.C.8A

CCSS.HSA-SSE.B.3B

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 is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, b² - 4ac. It determines the nature of the roots: if positive, two distinct real roots; if zero, one real root; if negative, no real roots.

Tags

CCSS.HSA-REI.B.4B