quadratic function graphs

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the coefficient 'a' in a quadratic function determine?

Back

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

Tags

CCSS.HSF-IF.C.7A

Front

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

Back

To find the y-intercept, set x = 0 in the quadratic equation and solve for y.

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 the direction of the parabola.

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are coefficients from the quadratic equation.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (D = b² - 4ac) determines the nature of the roots: if D > 0, there are two distinct real roots; if D = 0, there is one real root; if D < 0, there are no real roots.

Tags

CCSS.HSA-REI.B.4B

Front

What shape do quadratic functions create when graphed?

Back

Quadratic functions create a parabolic shape when graphed.

Tags

CCSS.HSF-IF.C.7A

Front

What are the coordinates of the vertex for the quadratic function y = ax² + bx + c?

Back

The coordinates of the vertex can be found using the formula (h, k), where h = -b/(2a) and k = f(h).

Front

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

Back

If the coefficient 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the formula for finding the roots of a quadratic equation?

Back

The roots can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B