Axis of Symmetry, Vertex...

Front

What determines if a parabola opens up or down?

Back

The coefficient 'a' in the quadratic equation determines the direction of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

Front

What is the axis of symmetry for the parabola represented by the equation y = 3x² - 6x + 4?

Back

The axis of symmetry is x = 1, which can be found using the formula x = -b/(2a) where a = 3 and b = -6.

Front

How do you find the vertex of the function f(x) = -x² - 4x + 12?

Back

The vertex can be found using the formula x = -b/(2a). For this function, a = -1 and b = -4, so the vertex is (-2, 16).

Front

What is the equation for the axis of symmetry?

Back

The axis of symmetry for a parabola in the form y = ax² + bx + c is given by the equation x = -b/(2a).

Front

Identify the values of a, b, and c in the equation 3x² + 4 = 5x.

Back

In the equation 3x² - 5x + 4 = 0, the values are a = 3, b = -5, and c = 4.

Front

What is the vertex form of a quadratic function?

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

How can you determine the direction of a parabola from its equation?

Back

By examining the coefficient 'a' in the quadratic equation y = ax² + bx + c. If 'a' > 0, it opens upwards; if 'a' < 0, it opens downwards.

Front

What is the significance of the vertex in a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its direction. It represents the maximum or minimum value of the function.

Front

How do you convert standard form to vertex form?

Back

To convert from standard form y = ax² + bx + c to vertex form, complete the square.

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 x = -b/(2a) back into the original equation.