Graphing Quadratics in Vertex Form

Front

What causes the graph of y = x² to open downward?

Back

Multiply the x² by a negative number.

Front

What is the graph of a quadratic function called?

Back

Parabola.

Front

What are the zeros/roots/solutions of the function x² + 3?

Back

There are none. It does not cross the x-axis.

Front

What is the green dot on the parabola called?

Back

Maximum.

Front

Given: y = 2(x - 5)² + 6, what is the vertex?

Back

(5,6).

Front

What is the vertex form of a quadratic function?

Back

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

Front

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

Back

If 'a' is positive, the parabola opens upward; if 'a' is negative, it opens downward.

Front

How do you find the axis of symmetry for a quadratic in vertex form?

Back

x = h, where (h, k) is the vertex.

Front

What is the significance of the vertex in a parabola?

Back

It represents the maximum or minimum point of the graph.

Front

How can you determine if a quadratic function has real roots?

Back

By calculating the discriminant (b² - 4ac); if it's positive, there are two real roots; if zero, one real root; if negative, no real roots.