How do you identify the transformations from the equation $$y = (x - 3)^2 + 4$$ ?

This equation represents a translation right by 3 units and up by 4 units from the parent function $$y = x^2$$ .

What does the term 'horizontal translation' refer to?

Horizontal translation refers to shifting the graph left or right. In the equation $$y = (x + h)^2$$ , the graph shifts left by $$h$$ units.

What is the effect of adding a constant to a quadratic function?

Adding a constant to a quadratic function shifts the graph vertically. For example, $$y = x^2 + k$$ shifts the graph up by $$k$$ units if $$k > 0$$ and down if $$k

What is the standard form of a quadratic function?

The standard form of a quadratic function is $$y = ax^2 + bx + c$$ , where $$a$$ , $$b$$ , and $$c$$ are constants.

What is the vertex form of a quadratic function?

The vertex form of a quadratic function is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

How do you determine the axis of symmetry for a quadratic function?

The axis of symmetry can be found using the formula $$x = -\frac{b}{2a}$$ from the standard form $$y = ax^2 + bx + c$$ .

What is the significance of the discriminant in a quadratic equation?

The discriminant, given by $$D = b^2 - 4ac$$ , determines the nature of the roots of the quadratic equation: if $$D > 0$$ , there are two distinct real roots; if $$D = 0$$ , there is one real root; if $$D

What transformations occur in the equation $$y = -2(x + 1)^2 - 3$$ ?

This equation represents a reflection over the x-axis, a vertical stretch by a factor of 2, a translation left by 1 unit, and a translation down by 3 units.

Quadratic Transformations Review Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic function?

Back

2.

FLASHCARD QUESTION

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What does the coefficient 'a' in a quadratic function determine?

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