Vertex form and Identifying Graphs and Equations

Front

What is the vertex form of a quadratic equation?

Back

Front

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

Back

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

Front

How do you identify a quadratic function from a graph?

Back

A quadratic function has a U-shaped graph (parabola) that can open upwards or downwards.

Front

What does the 'h' term in the vertex form tell you?

Back

The 'h' term indicates the horizontal shift of the graph. It moves the graph left or right, opposite of the x-value of the vertex.

Front

What does the 'k' term in the vertex form tell you?

Back

The 'k' term indicates the vertical shift of the graph. It moves the graph up or down, representing the y-value of the vertex.

Front

How can you determine if a graph is linear, exponential, or quadratic?

Back

A linear graph is a straight line, an exponential graph increases or decreases rapidly, and a quadratic graph is U-shaped (parabola).

Front

Back

The vertex of the function is (2, 5).

Front

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

Back

Changing the 'a' value affects the width and direction of the parabola. A larger absolute value of 'a' makes the parabola narrower, while a smaller absolute value makes it wider.

Front

If a quadratic function has its vertex at (3, -2), what is the value of 'h'?

Back

'h' is 3, as it represents the x-coordinate of the vertex.

Front

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

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.