Roots, solutions, zeros from quadratic graph

Front

What are the zeros of a quadratic function?

Back

The zeros of a quadratic function are the values of x for which the function equals zero. They are the x-intercepts of the graph.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Front

How do you find the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using factoring, completing the square, or the quadratic formula: x = (-b ± √(b²-4ac)) / 2a.

Tags

CCSS.HSA-REI.B.4B

Front

What is the relationship between zeros and x-intercepts?

Back

Zeros and x-intercepts refer to the same points on the graph of a quadratic function where the graph crosses the x-axis.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean if a quadratic function has two distinct real zeros?

Back

It means the graph of the quadratic function intersects the x-axis at two different points.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean if a quadratic function has one real zero?

Back

It means the graph of the quadratic function touches the x-axis at one point (the vertex) and does not cross it.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean if a quadratic function has no real zeros?

Back

It means the graph of the quadratic function does not intersect the x-axis at all, indicating that the solutions are complex numbers.

Tags

CCSS.HSF-IF.C.7A

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 ax² + bx + c = 0.

Tags

CCSS.HSA-REI.B.4B

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 the direction of the parabola.

Front

How can you determine the direction of a parabola?

Back

The direction of a parabola is determined by the sign of the coefficient 'a' in the quadratic equation y = ax² + bx + c. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

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).