(Alg.2) 4.1 (Flashcard) Quadratics Functions.

Front

What is the equation for the axis of symmetry in a quadratic function?

Back

The equation for the axis of symmetry is x = -b/(2a), where a and b are coefficients from the quadratic equation in the form y = ax^2 + bx + c.

Front

What is the vertex of the quadratic function y = ax^2 + bx + c?

Back

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

Front

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

Back

Set y = 0 in the equation ax^2 + bx + c = 0 and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax^2 + bx + c.

Front

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

Back

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

Front

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

Back

The discriminant (D = b^2 - 4ac) determines the nature of the roots: D > 0 means two real roots, D = 0 means one real root, and D < 0 means no real roots.

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.

Front

What is the vertex form of a quadratic function?

Back

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

Front

What is the axis of symmetry for the function y = x^2 - 6x + 8?

Back

The axis of symmetry is x = 3.

Front

How do you convert from standard form to vertex form?

Back

Complete the square on the quadratic expression to rewrite it in the form y = a(x - h)^2 + k.