Writing Quadratics in Vertex and Intercept Form

Front

What is the vertex form of a quadratic function?

Back

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

Front

What is the intercept form of a quadratic function?

Back

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

Front

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

Back

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

Front

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

Back

The 'a' value determines 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 axis of symmetry (a.o.s.) in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves, given by the equation x = h, where h is the x-coordinate of the vertex.

Front

How do you determine the domain of a quadratic function?

Back

The domain of a quadratic function is all real numbers, as there are no restrictions on the input values.

Front

How do you determine the range of a quadratic function that opens upwards?

Back

For a quadratic function that opens upwards, the range is from the y-coordinate of the vertex to positive infinity: [k, ∞), where (h, k) is the vertex.

Front

How do you determine the range of a quadratic function that opens downwards?

Back

For a quadratic function that opens downwards, the range is from negative infinity to the y-coordinate of the vertex: (-∞, k], where (h, k) is the vertex.

Front

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

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, and they can be found by setting y = 0 and solving for x.

Front

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

Back

To convert from standard form y = ax² + bx + c to vertex form, complete the square.