Vertex Form Quadratic Equations

Front

What is the vertex form of a quadratic equation?

Back

y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

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

Back

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

Front

How does changing 'h' in the vertex form affect the graph?

Back

Changing 'h' shifts the graph horizontally. If 'h' increases, the graph shifts to the right; if 'h' decreases, it shifts to the left.

Front

How does changing 'k' in the vertex form affect the graph?

Back

Changing 'k' shifts the graph vertically. If 'k' increases, the graph shifts up; if 'k' decreases, it shifts down.

Front

What is the effect of a negative 'a' value in the vertex form?

Back

A negative 'a' value reflects the graph across the x-axis.

Front

What is the vertex of the quadratic function y = 2(x + 3)² - 4?

Back

The vertex is (-3, -4).

Front

What transformation occurs when the equation y = (x - 1)² + 5 is graphed?

Back

The graph is shifted 1 unit right and 5 units up from the parent function y = x².

Front

What is the parent function of a quadratic equation?

Back

The parent function is y = x², which is the simplest form of a quadratic function.

Front

How do you identify the vertex from the vertex form?

Back

The vertex is given by the point (h, k) in the equation y = a(x - h)² + k.

Front

What does it mean for a parabola to be 'compressed' or 'stretched'?

Back

A parabola is 'compressed' if the absolute value of 'a' is less than 1, making it wider. It is 'stretched' if the absolute value of 'a' is greater than 1, making it narrower.