What is the axis of symmetry in a quadratic function?

The axis of symmetry is a vertical line that passes through the vertex of the parabola, given by the equation $$x = -\frac{b}{2a}$$ .

What is the quadratic formula used for?

The quadratic formula is used to find the roots (x-intercepts) of a quadratic equation and is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What does the discriminant of a quadratic equation tell us?

The discriminant, given by $$b^2 - 4ac$$ , indicates the nature of the roots: if positive, there are two real roots; if zero, one real root; if negative, no real roots.

What is the vertex form of a quadratic equation?

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

How can you convert from standard form to vertex form?

To convert from standard form to vertex form, complete the square on the quadratic expression.

What is the effect of changing the value of 'a' in the vertex form $$y = a(x - h)^2 + k$$ ?

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

What is the relationship between the roots and the vertex of a parabola?

The vertex lies on the axis of symmetry, which is equidistant from the roots of the parabola.

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.

Graphing Quadratics in Standard Form Homework Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

Back

The variable 'a' represents the coefficient of the quadratic term and determines the direction and width of the parabola.

3.

FLASHCARD QUESTION

Front

What is the formula for finding the x-value of the vertex of a quadratic equation?

Back

4.

FLASHCARD QUESTION

Front

What does the vertex of a parabola represent?

Back

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

5.

FLASHCARD QUESTION

Front

How can you determine if a parabola opens upwards or downwards?

Back

6.

FLASHCARD QUESTION

Front

What is the significance of the 'c' value in the quadratic equation?

Back

The 'c' value represents the y-intercept of the parabola, which is the point where the graph crosses the y-axis.

7.

FLASHCARD QUESTION

Front

How do you find the y-value of the vertex using the x-value?

Back

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