Review of Graphing Quadratics in Vertex and Standard Form

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a) for a quadratic in standard form f(x) = ax^2 + bx + c.

Front

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

Back

The vertex can be found using the formula x = -b/(2a) to find the x-coordinate, and then substituting this value back into the function to find the y-coordinate.

Front

What is the vertex of the function f(x) = x^2 - 4x + 4?

Back

The vertex is (2, 0).

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is the vertex form of a quadratic function?

Back

The vertex form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

Front

How do you convert from standard form to vertex form?

Back

To convert from standard form to vertex form, you can complete the square.

Front

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

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

Front

What is the y-intercept of a quadratic function?

Back

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

Front

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

Back

The x-intercepts can be found by setting f(x) = 0 and solving 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.