Quadratics and Linear Functions

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

Front

How do you find the vertex of a quadratic function in standard form?

Back

To find the vertex of a quadratic function in standard form f(x) = ax² + bx + c, use the formula h = -b/(2a) and then calculate k by substituting h back into the function.

Front

What does completing the square mean in relation to quadratic functions?

Back

Completing the square is a method used to convert a quadratic function from standard form to vertex form by rewriting it as a perfect square trinomial.

Front

What is the minimum value of a quadratic function?

Back

The minimum value of a quadratic function occurs at the vertex if the parabola opens upwards (a > 0).

Front

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

Back

The 'a' value determines the direction of the parabola: if a > 0, it opens upwards; if a < 0, it opens downwards.

Tags

CCSS.HSF-IF.C.7A

Front

What is the FOIL method used for?

Back

The FOIL method is used to multiply two binomials and stands for First, Outside, Inside, Last.

Tags

CCSS.HSA.APR.A.1

Front

How do you convert a quadratic function from intercept form to vertex form?

Back

To convert from intercept form f(x) = a(x-p)(x-q) to vertex form, find the vertex (h, k) using h = (p+q)/2 and k = f(h).

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, given by the equation x = h, where h is the x-coordinate of the vertex.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

How do you determine the x-intercepts of a quadratic function?

Back

To find the x-intercepts of a quadratic function, set f(x) = 0 and solve the resulting quadratic equation.

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A