What does the discriminant of a quadratic equation tell you?

The discriminant, given by $$D = b^2 - 4ac$$ , indicates 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 (a repeated root); if $$D

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 $$y = ax^2 + bx + c$$ to vertex form $$y = a(x - h)^2 + k$$ , complete the square.

What is the significance of the vertex in a parabola?

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

How do you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, y-intercept, and x-intercepts. Plot these points and draw a smooth curve through them.

What is the relationship between the coefficients and the graph of a quadratic function?

The coefficients $$a$$ , $$b$$ , and $$c$$ affect the shape, position, and direction of the parabola. For example, $$a$$ determines the width and direction of opening, while $$b$$ and $$c$$ affect the position.

What are the key features to identify when graphing quadratics?

Key features to identify when graphing quadratics include the vertex, axis of symmetry, y-intercept, x-intercepts, and the direction of opening.

How do you find the maximum or minimum value of a quadratic function?

The maximum or minimum value of a quadratic function $$y = ax^2 + bx + c$$ occurs at the vertex, which can be found using $$x = -\frac{b}{2a}$$ . Substitute this x-value back into the function to find the corresponding y-value.

7.2-Graphing Quadratics Flashcard

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

How do you find the vertex of a parabola given in standard form?

Back

3.

FLASHCARD QUESTION

Front

What is the axis of symmetry for a parabola?

Back

4.

FLASHCARD QUESTION

Front

How do you determine the direction of opening for a parabola?

Back

Tags

CCSS.HSF-IF.C.7A

5.

FLASHCARD QUESTION

Front

What is the y-intercept of a quadratic function?

Back

Tags

CCSS.HSF-IF.C.7A

6.

FLASHCARD QUESTION

Front

How do you find the x-intercepts (zeros) of a quadratic function?

Back

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

7.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

Tags

CCSS.HSA-REI.B.4B

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