Graphing quadratics from vertex 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 find the vertex from the standard form of a quadratic equation?

Back

To find the vertex from the standard form y = ax² + bx + c, use the formula h = -b/(2a) and k = f(h).

Front

What does the 'a' value in the vertex form indicate about the parabola?

Back

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and its width (narrower if |a| > 1, wider if |a| < 1).

Front

What is the axis of symmetry 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, k) is the vertex.

Front

What is the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value of a quadratic function occurs at the vertex. It is a maximum if the parabola opens downward (a < 0) and a minimum if it opens upward (a > 0).

Front

What is a parabola?

Back

A parabola is the graph of a quadratic function, which is U-shaped and can open either upward or downward.

Front

What are the roots of a quadratic equation?

Back

The roots of a quadratic equation are the x-values where the graph intersects the x-axis, also known as the solutions of the equation.

Front

How do you determine if the vertex is a maximum or minimum?

Back

If the 'a' value in the vertex form is negative, the vertex is a maximum. If 'a' is positive, the vertex is a minimum.

Front

What is the significance of the vertex in graphing quadratics?

Back

The vertex is the highest or lowest point of the parabola and is crucial for sketching the graph accurately.

Front

What is the formula for finding the axis of symmetry?

Back

The formula for the axis of symmetry is x = -b/(2a) for a quadratic in standard form.