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

Front

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

Back

The axis of symmetry is given by the equation x = -\frac{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 a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, found at the coordinates (h, k) where h = -\frac{b}{2a} and k is the value of the function at h.

Front

How do you find the axis of symmetry for the function y = 2x^2 + 4x + 1?

Back

The axis of symmetry can be found using the formula x = -\frac{b}{2a}. Here, a = 2 and b = 4, so x = -\frac{4}{2(2)} = -1.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

Front

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

Back

A quadratic function opens upwards if the coefficient a > 0 and downwards if a < 0.

Front

What is the formula to find the y-coordinate of the vertex?

Back

The y-coordinate of the vertex can be found by substituting h into the function: k = f(h) = a(h^2) + b(h) + c.

Front

What are the values of a, b, and c in the quadratic equation y = 3x^2 - 5x + 2?

Back

In this equation, a = 3, b = -5, and c = 2.

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 distinct real roots, D = 0 means one real root, and D < 0 means no real roots.

Front

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

Back

The x-intercepts can be found by setting y = 0 and solving the equation ax^2 + bx + c = 0 using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, used to find the roots of the quadratic equation ax^2 + bx + c = 0.