How do you find the vertex of the quadratic function: $$f(x)=x^2+6x+13$$ ?

To find the vertex, use the formula $$x=-\frac{b}{2a}$$ . Here, $$a=1$$ and $$b=6$$ , so $$x=-\frac{6}{2(1)}=-3$$ . Substitute $$x=-3$$ back into the function to find the y-coordinate: $$f(-3)=(-3)^2+6(-3)+13=4$$ . Thus, the vertex is (-3, 4).

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.

What does it mean for a quadratic function to open upwards?

A quadratic function opens upwards if the coefficient $$a$$ in the standard form $$f(x)=ax^2+bx+c$$ is positive (i.e., $$a > 0$$ ). This means the vertex is a minimum point.

What does it mean for a quadratic function to open downwards?

A quadratic function opens downwards if the coefficient $$a$$ in the standard form $$f(x)=ax^2+bx+c$$ is negative (i.e., $$a

How do you determine if a quadratic function has a maximum or minimum?

To determine if a quadratic function has a maximum or minimum, check the sign of the coefficient $$a$$ in the standard form. If $$a > 0$$ , it has a minimum; if $$a

What is the axis of symmetry in a quadratic function?

The axis of symmetry of a quadratic function is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula $$x=-\frac{b}{2a}$$ .

What is the significance of the vertex in a quadratic function?

The vertex of a quadratic function represents the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards.

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

Changing the value of $$a$$ in a quadratic function affects the width and direction of the parabola. A larger absolute value of $$a$$ makes the parabola narrower, while a smaller absolute value makes it wider.

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

The roots (or x-intercepts) of a quadratic function are the points where the graph intersects the x-axis. The vertex lies on the axis of symmetry, which is equidistant from the roots.

9.1 - 9.4 Flashcard Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Range of a function?

Back

2.

FLASHCARD QUESTION

Front

What does Maximum or Minimum refer to in a quadratic function?

Back

Maximum or Minimum refers to the highest or lowest point on the graph of a quadratic function. A Minimum occurs at the vertex of the parabola when it opens upwards.

3.

FLASHCARD QUESTION

Front

How do you find the vertex of a quadratic function given in vertex form?

Back

4.

FLASHCARD QUESTION

Front

What is the Domain of a function?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is a quadratic function?

Back

7.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic function?

Back

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