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2 years ago

How to determine the direction a parabola opens

Mathematics

1 answer:

kozerog [31]2 years ago

5 0

Answer:

Upward or Downward

Step-by-step explanation:

A parabola is the graph of a quadratic function y = ax2 + bx + c. The graphs below depict two typical parabolas:

For clarity, we indicate their x-intercepts with red dots, their y-intercepts with pink dots, and the vertex of each parabola with a green dot:

The first parabola (a U shape) opens vertically, whereas the second parabola opens downwards (is an upside down U shape).

Given the function y = ax2 + bx + c, write the following:

If an is greater than zero (positive), the parabola widens upward.
If the value is 0 (negative), the parabola expands downward.

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Which of the following best describes the equation below?

sergiy2304 [10]

Answer:

both linear and nonlinear

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3 years ago

Which expression is equivalent to -1.3-(-1.9)

alex41 [277]

-1.3+1.9=.6
the two minus signs turn into a plus so you add 1.9 to -1.3

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3 years ago

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Which two values are greater than 3/5 1/4 0.68 2/3 0.599 1/2

kodGreya [7K]

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3 years ago

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Let F(x) = x^2 – 15 and G(x)= 4 - x Find (F/G)(–7) =

KATRIN_1 [288]

Answer:

$\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{34}{11}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Functions
Function Notation

Step-by-step explanation:

Step 1: Define

Identify

F(x) = x² - 15

G(x) = 4 - x

Step 2: Find

Substitute in functions: $\displaystyle \bigg( \frac{F}{G} \bigg)(x) = \frac{x^2 - 15}{4 - x}$

Step 3: Evaluate

Substitute in x [Function (F/G)(x)]: $\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{(-7)^2 - 15}{4 - (-7)}$
Exponents: $\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{49 - 15}{4 - (-7)}$
Subtract: $\displaystyle \bigg( \frac{F}{G} \bigg)(-7) = \frac{34}{11}$

8 0

3 years ago

A scientist need 10 liters of a 20% acid solution for an experiment, but she only has a 5% soliution and a 40% solution. To the

Stolb23 [73]

Answer:

5.7 liters of 5% solution and 4.3 liters of 40% solution is needed to be mixed to get 10 liters of a 20% acid solution

Step-by-step explanation:

Let

x = Amount of 5% solution needed

(10 - x) = Amount of 40% solution needed

Equation:

5% of x + 40% of (10-x) = 20% of 10

0.05x + 0.40(10-x) = 0.20 * 10

Open parenthesis

0.05x + 4.0 - 0.40x = 0.20 * 10

Collect like terms

4.0 - 0.35x = 2.0

Add 0.35x to both sides of the equation

4.0 = 2.0 + 0.35x

Subtract 2.0 from both sides of the equation

2.0 = 0.35x

Divide both sides by 0.35

2.0 / 0.35 =x

5.7 = x

5.7 liter of the 5% solution is needed

Next is to find the amount of 40% solution needed

(10 - x) = Amount of 40% solution used

Amount of 40% solution used = 10 - 5.7

= 4.3

4.3 liters of 40% solution is needed

6 0

3 years ago