Vertex and Standard Form

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 identify the vertex from the vertex form of a quadratic equation?

Back

The vertex (h, k) can be identified directly from the vertex form y = a(x - h)² + k.

Front

What does the 'a' value in the vertex form 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.

Front

What is the standard form of a quadratic equation?

Back

The standard form of a quadratic equation is given by y = ax² + bx + c.

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 and simplify to the form y = ax² + bx + c.

Front

What is the significance of the 'c' value in the standard form of a quadratic equation?

Back

The 'c' value represents the y-intercept of the quadratic function.

Front

How do you find the y-intercept from the standard form of a quadratic equation?

Back

The y-intercept can be found by evaluating the function at x = 0, which gives y = c.

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.

Front

How do you find the maximum or minimum value of a quadratic function in vertex form?

Back

The maximum or minimum value occurs at the vertex (h, k), where k is the maximum or minimum value depending on the sign of 'a'.

Front

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

Back

The roots of a quadratic equation are the x-intercepts of the graph, where the parabola crosses the x-axis.