Graphing Quadratic Equations

Front

What is the range of a quadratic function with a vertex at (h, k) where k is the minimum value?

Back

The range is y ≥ k.

Tags

CCSS.HSF-IF.C.7A

Front

What is the axis of symmetry for a quadratic function in the form y = ax^2 + bx + c?

Back

The axis of symmetry is x = -b/(2a).

Front

What are the coordinates of the vertex of a parabola given by the equation y = ax^2 + bx + c?

Back

The vertex coordinates are (-b/(2a), f(-b/(2a))).

Front

How do you find the y-intercept of a quadratic function?

Back

Set x = 0 in the equation y = ax^2 + bx + c.

Tags

CCSS.HSF-IF.C.7A

Front

What is the general shape of a quadratic graph?

Back

A parabola, which opens upwards if a > 0 and downwards if a < 0.

Tags

CCSS.HSF-IF.C.7A

Front

What does the 'a' value in the quadratic equation y = ax^2 + bx + c determine?

Back

It determines the direction and width of the parabola.

Tags

CCSS.HSF-IF.C.7A

Front

If a quadratic function has no real roots, what can be said about its graph?

Back

The graph does not intersect the x-axis.

Tags

CCSS.HSF-IF.C.7A

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex represents the maximum or minimum point of the graph.

Front

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

Back

By the sign of 'a': if a > 0, it opens upwards; if a < 0, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the formula to find the roots of a quadratic equation?

Back

x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B