Transformations Of Quadratics

Front

What is the parent function of a quadratic?

Back

The parent function of a quadratic is y = x².

Front

What transformation occurs when the graph of y = x² is reflected over the x-axis?

Back

The transformation results in the graph of y = -x².

Front

How does the graph of y = -3x² differ from the graph of y = x²?

Back

The graph of y = -3x² is a reflection over the x-axis and is narrower than the graph of y = x².

Front

What does a horizontal shift of 4 units to the left do to the graph of f(x) = x²?

Back

It transforms the graph to g(x) = (x + 4)².

Front

If the blue graph is f(x) = x², what is the equation of the red graph that represents a shift to the right by 3 units?

Back

The equation of the red graph is g(x) = (x - 3)².

Front

What effect does multiplying a quadratic function by a negative number have on its graph?

Back

It reflects the graph over the x-axis.

Front

What is the effect of a vertical stretch on the graph of a quadratic function?

Back

A vertical stretch makes the graph narrower.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax² + bx + c.

Front

What does the vertex of a quadratic function represent?

Back

The vertex represents the highest or lowest point of the graph, depending on the direction it opens.

Front

How can you determine the direction in which a quadratic opens?

Back

If the coefficient 'a' in y = ax² is positive, the graph opens upwards; if 'a' is negative, it opens downwards.