Writing Quadratics from Vertex and from Points

Front

What is the vertex form of a quadratic function?

Back

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

Front

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

Back

To find the vertex of a quadratic function in standard form y = ax² + bx + c, use the formula h = -b/(2a) for the x-coordinate, and then substitute h back into the function to find k.

Front

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

Back

The vertex represents the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

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.

Front

What does the 'a' value in the vertex form of a quadratic function indicate?

Back

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

Front

What is the process to determine a quadratic function given its vertex and a point?

Back

Substitute the vertex coordinates into the vertex form to find 'a' using the given point, then write the function.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax² + bx + c.

Front

How do you identify the axis of symmetry for a quadratic function?

Back

The axis of symmetry can be found using the formula x = -b/(2a) from the standard form of the quadratic function.

Front

What is the relationship between the roots of a quadratic function and its graph?

Back

The roots (or x-intercepts) of a quadratic function are the points where the graph intersects the x-axis.

Front

How can you find the roots of a quadratic function in standard form?

Back

You can find the roots using the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).