Quadratic Review

Front

What is the axis of symmetry for a quadratic function in vertex form?

Back

The axis of symmetry for a quadratic function in vertex form, y = a(x-h)² + k, is the vertical line x = h.

Front

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

Back

The vertex of a quadratic function in vertex form, y = a(x-h)² + k, is the point (h, k).

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

How do you convert a quadratic function from vertex form to standard form?

Back

To convert from vertex form y = a(x-h)² + k to standard form, expand the equation to the form y = ax² + bx + c.

Front

What is the significance of the x-intercepts of a quadratic function?

Back

The x-intercepts of a quadratic function are the points where the graph intersects the x-axis, indicating the values of x for which y = 0.

Front

How do you determine the maximum height of a projectile modeled by a quadratic function?

Back

The maximum height of a projectile can be found by determining the vertex of the quadratic function, which occurs at t = -b/(2a) for the function h(t) = at² + bt + c.

Front

What is the formula to find the vertex of a quadratic function given in standard form?

Back

The vertex (h, k) of a quadratic function in standard form f(x) = ax² + bx + c can be found using h = -b/(2a) and k = f(h).

Front

What does the coefficient 'a' indicate in a quadratic function?

Back

The coefficient 'a' in a quadratic function determines the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola.

Front

How can you find the roots of a quadratic equation?

Back

The roots of a quadratic equation can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

Front

What is the relationship between the vertex and the axis of symmetry in a quadratic function?

Back

The vertex lies on the axis of symmetry, which is a vertical line that divides the parabola into two mirror-image halves.