Graphing Quadratics

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation. It can be found using the formula x = -b/(2a) for the quadratic equation in the form y = ax^2 + bx + c.

Front

How do you find the vertex of the quadratic function y = -2x^2 + 4x + 3?

Back

The vertex is (1, 5). Use the formula x = -b/(2a) to find x = -4/(2*-2) = 1, then substitute x back into the equation to find y.

Front

What is the vertex of the quadratic function y = x^2 + 16x + 71?

Back

The vertex is V(-8, 7). Use the formula x = -b/(2a) to find x = -16/(2*1) = -8, then substitute x back into the equation to find y.

Front

What is the vertex of the quadratic function y = x^2 - 8x + 14?

Back

The vertex is (4, -2). Use the formula x = -b/(2a) to find x = 8/(2*1) = 4, then substitute x back into the equation to find y.

Front

What is the vertex of the parabola represented by the equation y = -x^2 + 2x + 3?

Back

The vertex is (1, 4). Use the formula x = -b/(2a) to find x = -2/(-2) = 1, then substitute x back into the equation to find y.

Front

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

Back

The y-intercept is found by evaluating the function at x = 0. For example, in y = x^2 - 6x + 5, the y-intercept is (0, 5).

Front

What is the y-intercept of the quadratic function y = x^2 - 6x + 5?

Back

The y-intercept is (0, 5). Substitute x = 0 into the equation to find y.

Front

What is the standard form of a quadratic function?

Back

The standard form is y = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the 'a' value in a quadratic function 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 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).