Intro to Finding the Vertex Given Standard Form of Quadratics

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

How do you find the x-coordinate of the vertex of a quadratic function in standard form?

Back

The x-coordinate of the vertex can be found using the formula x = -b/(2a).

Front

Given the quadratic equation y = 3x² - 12x + 7, identify a, b, and c.

Back

a = 3, b = -12, c = 7.

Front

What does the vertex of a parabola represent?

Back

The vertex represents the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

If a > 0 in the standard form of a quadratic equation, what direction does the parabola open?

Back

The parabola opens upwards.

Front

If a < 0 in the standard form of a quadratic equation, what direction does the parabola open?

Back

The parabola 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).

Front

How do you find the y-coordinate of the vertex after finding the x-coordinate?

Back

Substitute the x-coordinate back into the original quadratic equation to find the corresponding y-coordinate.

Front

What is the vertex of the quadratic function y = 2x² - 8x + 6?

Back

The vertex is (2, -2).

Front

What is the significance of the coefficients a, b, and c in the standard form of a quadratic equation?

Back

Coefficient a determines the direction and width of the parabola, b affects the position of the vertex, and c is the y-intercept.