Writing in different quadratic forms

Front

What is the vertex form of a quadratic equation?

Back

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

Front

How do you convert from vertex form to standard form?

Back

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

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.

Front

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

Back

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

Front

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

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens. It represents the maximum or minimum value of the function.

Front

How do you find the vertex from standard form?

Back

To find the vertex from standard form y = ax² + bx + c, use the formula h = -b/(2a) and then substitute h back into the equation to find k.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation x = h, where (h, k) is the vertex.

Front

How do you convert from standard form to vertex form?

Back

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

Front

What are the x-intercepts of a quadratic function?

Back

The x-intercepts are the points where the graph of the quadratic function crosses the x-axis, found by solving the equation ax² + bx + c = 0.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation: x = (-b ± √(b² - 4ac)) / (2a).