Quadratics - Standard Form

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, found by evaluating f(0).

Front

How do you find the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form f(x) = ax² + bx + c.

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 upwards or downwards.

Front

How do you determine if a quadratic function has a maximum or minimum value?

Back

If a > 0, the parabola opens upwards and has a minimum value. If a < 0, it opens downwards and has a maximum value.

Front

What are the roots of a quadratic equation?

Back

The roots are the values of x where the quadratic function equals zero, found by solving the equation ax² + bx + c = 0.

Front

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

Back

The discriminant (D = b² - 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 can you find the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value can be found by evaluating the function at the vertex, using the vertex formula x = -b/(2a).

Front

What does it mean for a quadratic function to be in vertex form?

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

What is the effect of the coefficient 'a' in a quadratic function?

Back

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