Vertex Form Quadratics

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

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

Back

The 'a' value indicates the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if negative, it opens downwards. A larger absolute value of 'a' indicates a narrower parabola.

Front

How do you find the vertex from the vertex form?

Back

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

Front

How does shifting a graph vertically affect its equation?

Back

Shifting a graph vertically affects the 'k' value in the vertex form. For example, shifting up by 3 units changes y = a(x-h)² + k to y = a(x-h)² + (k+3).

Front

What transformation occurs when 'h' is negative in the vertex form?

Back

When 'h' is negative, the graph shifts to the right. For example, y = a(x+2)² + k shifts the graph 2 units to the left.

Front

What is the effect of a negative 'a' value on the graph of a quadratic function?

Back

A negative 'a' value reflects the graph across the x-axis, making the parabola open downwards.

Front

How do you determine the y-intercept from the vertex form?

Back

To find the y-intercept, set x = 0 in the vertex form equation and solve for y.

Front

What does it mean to 'stretch' a graph?

Back

A 'stretch' occurs when the absolute value of 'a' is greater than 1, making the parabola narrower.

Front

What does it mean to 'shrink' a graph?

Back

A 'shrink' occurs when the absolute value of 'a' is between 0 and 1, making the parabola wider.