How do you convert a quadratic function from vertex form to standard form?

To convert from vertex form $$f(x) = a(x-h)^2 + k$$ to standard form, expand the equation: $$f(x) = a(x^2 - 2hx + h^2) + k$$ .

What is the vertex form of a quadratic function?

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

How do you find the y-intercept of a quadratic function?

The y-intercept can be found by evaluating the function at $$x = 0$$ , which gives $$f(0) = c$$ in the standard form $$f(x) = ax^2 + bx + c$$ .

What is the relationship between the roots and the vertex of a quadratic function?

The vertex lies on the axis of symmetry, which is equidistant from the roots of the quadratic function. The x-coordinate of the vertex is the average of the roots.

What is the discriminant of a quadratic equation?

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

How do you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, y-intercept, and plot additional points. Then, draw a smooth curve through these points.

What is the effect of changing the value of 'b' in a quadratic function?

Changing the value of 'b' affects the position of the vertex and the axis of symmetry, but does not change the direction of the parabola.

What is the effect of changing the value of 'c' in a quadratic function?

Changing the value of 'c' shifts the graph vertically. It affects the y-intercept but does not change the shape or direction of the parabola.

Properties of Quadratic Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic function?

Back

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic function?

Back

3.

FLASHCARD QUESTION

Front

What is the vertex of a quadratic function?

Back

4.

FLASHCARD QUESTION

Front

How do you find the vertex from the standard form?

Back

5.

FLASHCARD QUESTION

Front

What is the axis of symmetry in a quadratic function?

Back

6.

FLASHCARD QUESTION

Front

What is the significance of the coefficient 'a' in a quadratic function?

Back

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