Parabola Features

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped curve that represents the graph of a quadratic function. It can open upwards or downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What are the x-intercepts of a parabola?

Back

The x-intercepts (or roots) of a parabola are the points where the graph intersects the x-axis, meaning the y-coordinate is zero.

Tags

CCSS.HSF-IF.C.7A

Front

What is the y-intercept of a parabola?

Back

The y-intercept of a parabola is the point where the graph intersects the y-axis, meaning the x-coordinate is zero.

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 upwards or downwards.

Front

How do you find the axis of symmetry of a parabola?

Back

The axis of symmetry of a parabola can be found using the formula x = -b/(2a) from the quadratic equation ax^2 + bx + c.

Front

What does it mean if a parabola has two roots?

Back

If a parabola has two roots, it means it intersects the x-axis at two distinct points.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean if a parabola has one root?

Back

If a parabola has one root, it means it touches the x-axis at exactly one point, also known as a double root.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean if a parabola has no roots?

Back

If a parabola has no roots, it means it does not intersect the x-axis at all.

Tags

CCSS.HSF-IF.C.7A

Front

How can you determine the direction a parabola opens?

Back

A parabola opens upwards if the coefficient of x^2 is positive and downwards if it is negative.

Tags

CCSS.HSF-IF.C.7A

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax^2 + bx + c.