Parts of a Parabola

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. It can be found using the formula x = -b/(2a) for a quadratic equation in the form 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 its orientation. It can be found using the formula (h, k) where h = -b/(2a) and k = f(h).

Front

How do you find the minimum value of a quadratic function?

Back

The minimum value of a quadratic function in the form f(x) = ax² + bx + c occurs at the vertex, calculated as k = f(h) where h = -b/(2a).

Front

What are x-intercepts of a parabola?

Back

The x-intercepts are the points where the parabola crosses the x-axis. They can be found by solving the equation ax² + bx + c = 0.

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 does the 'a' value in a quadratic equation indicate?

Back

The 'a' value determines the direction of the parabola. If a > 0, the parabola opens upwards; if a < 0, it opens downwards.

Front

What is the significance of the 'b' value in a quadratic equation?

Back

The 'b' value affects the position of the vertex along the x-axis and the steepness of the parabola.

Front

What is the significance of the 'c' value in a quadratic equation?

Back

The 'c' value represents the y-intercept of the parabola, which is the point where the graph crosses the y-axis.

Front

How can you determine if a quadratic function has real x-intercepts?

Back

You can determine this by calculating the discriminant (D = b² - 4ac). If D > 0, there are two real x-intercepts; if D = 0, there is one real x-intercept; if D < 0, there are no real x-intercepts.

Front

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

Back

The vertex (h, k) can be found using h = -b/(2a) and k = f(h), where f(h) is the value of the function at x = h.