Quadratics - Finding the vertex

Front

What is the U-shaped graph of a quadratic equation called?

Back

A parabola.

Front

What determines whether a parabola opens upwards or downwards?

Back

The sign of the coefficient of the x² term in the quadratic equation. If it's positive, the parabola opens upwards; if negative, it opens downwards.

Front

How do you find the vertex of a quadratic equation in standard form?

Back

Use the formula x = -b/(2a) to find the x-coordinate, then substitute it back into the equation to find the y-coordinate.

Front

What is the vertex of the quadratic equation y = 2x² - 16x + 33?

Back

(4, 1).

Front

What is the vertex of the quadratic equation y = 3x²?

Back

(0, 0).

Front

What is the standard form of a quadratic equation?

Back

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

Front

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

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and its width (larger |a| means a narrower parabola).

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation x = -b/(2a).

Front

How can you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex. If the parabola opens downwards, the vertex is a maximum; if it opens upwards, it's a minimum.

Front

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

Back

Changing the 'b' value affects the position of the vertex along the x-axis and the axis of symmetry.