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4 years ago

Is f(x)=x^2-2x+3 a quadratic function

Mathematics

2 answers:

Sav [38]4 years ago

6 0

Answer:

yes

Step-by-step explanation:

A quadratic function has the general form

fx) = ax² + bx + c ( a ≠ 0 )

f(x) = x² - 2x + 3 ← is in this form and is a quadratic function

Over [174]4 years ago

5 0

You learned this you should know

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Could someone please help me:) I am stick and I am not sure what to do

Delicious77 [7]

Answer:

Part 5.1.1:

$\displaystyle \cos 2A = \frac{7}{8}$

Part 5.1.2:

$\displaystyle \cos A = \frac{\sqrt{15}}{4}$

Step-by-step explanation:

We are given that:

$\displaystyle \sin 2A = \frac{\sqrt{15}}{8}$

Part 5.1.1

Recall that:

$\displaystyle \sin^2 \theta + \cos^2 \theta = 1$

Let θ = 2A. Hence:

$\displaystyle \sin ^2 2A + \cos ^2 2A = 1$

Square the original equation:

$\displaystyle \sin^2 2A = \frac{15}{64}$

Hence:

$\displaystyle \left(\frac{15}{64}\right) + \cos ^2 2A = 1$

Subtract:

$\displaystyle \cos ^2 2A = \frac{49}{64}$

Take the square root of both sides:

$\displaystyle \cos 2A = \pm\sqrt{\frac{49}{64}}$

Since 0° ≤ 2A ≤ 90°, cos(2A) must be positive. Hence:

$\displaystyle \cos 2A = \frac{7}{8}$

Part 5.1.2

Recall that:

$\displaystyle \begin{aligned} \cos 2\theta &= \cos^2 \theta - \sin^2 \theta \\ &= 1- 2\sin^2\theta \\ &= 2\cos^2\theta - 1\end{aligned}$

We can use the third form. Substitute:

$\displaystyle \left(\frac{7}{8}\right) = 2\cos^2 A - 1$

Solve for cosine:

$\displaystyle \begin{aligned} \frac{15}{8} &= 2\cos^2 A\\ \\ \cos^2 A &= \frac{15}{16} \\ \\ \cos A& = \pm\sqrt{\frac{15}{16}} \\ \\ \Rightarrow \cos A &= \frac{\sqrt{15}}{4}\end{aligned}$

In conclusion:

$\displaystyle \cos A = \frac{\sqrt{15}}{4}$

(Note that since 0° ≤ 2A ≤ 90°, 0° ≤ A ≤ 45°. Hence, cos(A) must be positive.)

4 0

3 years ago

4 Eric sketches a rectangle with a perimeter of

natka813 [3]

Answer:

2(x) + 2(x + 3) = 90

Step-by-step explanation:

Width: x inch.

Length: (x + 3) inch.

P = 2 $w^{}$ + 2 $l^{}$

P = 2(x) + 2(x + 3) = 90

7 0

3 years ago

Lexi needs 144 beads. A large box holds 100 beads. A medium box holds 10 beads. A small box holds 1 bead. Lexi already had 1 lar

Readme [11.4K]

She will need 4 medium boxes

7 0

3 years ago

PLS HELP HURRY BEFORE MY TEACHER COMES IN

Tresset [83]

Answer:

it is the hilighted one the one besides it and below it

Step-by-step explanation:

3 0

3 years ago

Write the simplified form of -64 1/3

Semenov [28]

Answer:

hope this helps

Step-by-step explanation:

To reduce a fraction to lowest terms (also called its simplest form), just divide both the numerator and denominator by the Greatest Common Factor (GCF or GCD). For example, 2/3 is in lowest form, but 4/6 is not in lowest form (the GCD of 4 and 6 is 2) and 4/6 can be expressed as 2/3.

8 0

3 years ago

Read 2 more answers