Graphing Quadratics in Vertex or Intercept Forms

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is given by the equation y = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you find the Axis of Symmetry for a quadratic function in factored form?

Back

For a quadratic function in factored form y = (x - p)(x - q), the Axis of Symmetry is found using the formula x = (p + q) / 2.

Front

What is 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 intercept form of a quadratic function?

Back

The intercept form of a quadratic function is written as y = a(x - p)(x - q), where p and q are the x-intercepts.

Front

How can you convert 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 get y = ax^2 - 2ahx + (ah^2 + k).

Front

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

Back

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

Front

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

Back

The y-intercept of a quadratic function can be found by evaluating the function at x = 0, which gives the point (0, c) in standard form y = ax^2 + bx + c.

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

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

Back

To find the x-intercepts of a quadratic function, set y = 0 and solve the equation ax^2 + bx + c = 0 using factoring, completing the square, or the quadratic formula.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), used to find the roots of the quadratic equation ax^2 + bx + c = 0.