Vertex Form to Standard 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

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 function?

Back

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

Front

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

Back

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

Front

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

Back

The vertex is the highest or lowest point of the parabola, representing the maximum or minimum value of the function.

Front

How can you find the vertex from the standard form of a quadratic function?

Back

The vertex can be found using the formula h = -b/(2a) and k = f(h), where f(h) is the function evaluated at h.

Front

What is a parabola?

Back

A parabola is the U-shaped graph of a quadratic function, which can open upwards or downwards.

Front

What is the y-intercept of a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

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

Back

The axis of symmetry can be found using the formula x = -b/(2a), which is a vertical line that divides the parabola into two mirror images.

Front

What is the relationship between the roots and the vertex of a parabola?

Back

The roots (x-intercepts) of a parabola can be found using the quadratic formula, and the vertex lies between the roots on the axis of symmetry.