Graphing Quadratics

Front

What is the vertex of the quadratic equation y = a(x - h)² + k?

Back

The vertex is the point (h, k) where the parabola reaches its maximum or minimum value.

Front

What is the axis of symmetry for a quadratic equation in the form y = ax² + bx + c?

Back

The axis of symmetry is given by the formula x = -b/(2a).

Front

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

Back

Convert to vertex form or use the formula x = -b/(2a) to find the x-coordinate, then substitute back to find the y-coordinate.

Front

What does the 'a' value in the quadratic equation y = ax² + bx + c indicate?

Back

The 'a' value determines the direction of the parabola (upward if a > 0, downward if a < 0) and its width.

Front

What is the range of a quadratic function that opens upwards?

Back

The range is y ≥ k, where (h, k) is the vertex.

Front

What is the range of a quadratic function that opens downwards?

Back

The range is y ≤ k, where (h, k) is the vertex.

Front

How do you determine if a quadratic function has a maximum or minimum value?

Back

If 'a' is positive, it has a minimum value; if 'a' is negative, it has a maximum value.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph crosses the y-axis, found by evaluating f(0).

Front

How can you find the x-intercepts of a quadratic function?

Back

Set the quadratic equation to zero and solve for x using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation.