9B Graph of Function

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped graph that represents a quadratic function. It can open upwards or downwards depending on the coefficient of the x² term.

Front

What is the standard form of a quadratic function?

Back

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

Front

What does the 'a' in the equation y = ax² + bx + c represent?

Back

The 'a' value determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards.

Front

What is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the y-intercept of a quadratic function?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What is the y-intercept of the function f(x) = 2x² + 4x + 6?

Back

The y-intercept is (0, 6).

Front

What is the axis of symmetry in a parabola?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = -b/(2a).

Front

What does the 'c' in the equation y = ax² + bx + c represent?

Back

The 'c' value represents the y-intercept of the parabola.

Front

What is the formula to find the vertex of a parabola given in standard form?

Back

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

Front

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

Back

The discriminant (b² - 4ac) determines the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.