Quadratic Graphs

Front

What is a parabola?

Back

A parabola is a symmetrical, curved shape that represents the graph of a quadratic function. It can open upwards or downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of a parabola, depending on its orientation.

Front

What does it mean if a parabola opens upwards?

Back

If a parabola opens upwards, it has a minimum value at its vertex.

Tags

CCSS.HSF-IF.C.7A

Front

What does it mean if a parabola opens downwards?

Back

If a parabola opens downwards, it has a maximum value at its vertex.

Tags

CCSS.HSF-IF.C.7A

Front

How do you find the x-intercepts of a parabola?

Back

The x-intercepts can be found by setting the quadratic equation to zero and solving for x.

Tags

CCSS.HSF-IF.C.7A

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, passing through the vertex.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

Front

What is the significance of the 'a' value in a quadratic equation?

Back

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

Tags

CCSS.HSF-IF.C.7A

Front

How can you determine if a parabola has a maximum or minimum value?

Back

You can determine this by looking at the 'a' value in the quadratic equation: if a > 0, it has a minimum; if a < 0, it has a maximum.

Tags

CCSS.HSF-IF.C.7A

Front

What is the formula to find the vertex of a parabola in standard form?

Back

The vertex can be found using the formula (-b/(2a), f(-b/(2a))) where f(x) is the quadratic function.