Quadratic Function In Standard Form

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is given by: f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

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

Back

The vertex (h, k) of the quadratic function f(x) = ax^2 + bx + c can be found using the formula: h = -b/(2a) and k = f(h).

Front

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

Back

The vertex represents the maximum or minimum point of the quadratic function, depending on the direction of the parabola (upward or downward).

Front

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

Back

A quadratic function opens upwards if the coefficient 'a' is positive (a > 0) and opens downwards if 'a' is negative (a < 0).

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept of a quadratic function f(x) = ax^2 + bx + c is the point where the graph intersects the y-axis, found by evaluating f(0) = c.

Front

How can you find the x-intercepts of a quadratic function?

Back

The x-intercepts can be found by solving the equation ax^2 + bx + c = 0 using factoring, completing the square, or the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation ax^2 + bx + c = 0 and is given by: x = (-b ± √(b^2 - 4ac)) / (2a).

Front

What does the discriminant of a quadratic function tell us?

Back

The discriminant, given by D = b^2 - 4ac, indicates the nature of the roots: D > 0 means two distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex and can be found by evaluating f(h) where h = -b/(2a).

Front

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

Back

To convert from standard form f(x) = ax^2 + bx + c to vertex form f(x) = a(x - h)^2 + k, complete the square.