Parabolas

Front

What is a parabola?

Back

A parabola is a symmetrical, U-shaped curve that can open upwards or downwards. It is the graph of a quadratic function.

Front

What is the standard form of a quadratic equation?

Back

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

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 axis of symmetry of a parabola?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form of the quadratic equation.

Front

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

Back

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

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 do you find the y-intercept of a parabola?

Back

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

Front

What is the formula for finding 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 h.

Front

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

Back

Changing the 'b' value affects the position of the vertex and the axis of symmetry of the parabola.

Front

What is the general shape of the graph of y = x²?

Back

The graph of y = x² is a parabola that opens upwards with its vertex at the origin (0,0).