Quadratics

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is ax² + bx + c = 0.

Front

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

Back

To find the y-intercept, set x = 0 in the function f(x) and solve for f(0).

Tags

CCSS.HSF-IF.C.7A

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the function crosses the x-axis, found by solving f(x) = 0.

Tags

CCSS.HSF-IF.C.7A

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens up or down.

Front

How can you determine if a parabola opens up or down?

Back

If the coefficient 'a' in the quadratic function f(x) = ax² + bx + c is positive, the parabola opens up; if 'a' is negative, it opens down.

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, passing through the vertex.

Front

What is the formula to find the vertex of a quadratic function?

Back

The vertex can be found using the formula x = -b/(2a) for the x-coordinate, and then substituting x back into the function to find the y-coordinate.

Front

What is the discriminant in a quadratic equation?

Back

The discriminant is the part of the quadratic formula under the square root, given by b² - 4ac, which determines the nature of the roots.

Tags

CCSS.HSA-REI.B.4B

Front

What does it mean if the discriminant is positive?

Back

If the discriminant is positive, the quadratic equation has two distinct real roots.

Tags

CCSS.HSA-REI.B.4B