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SSSSS [86.1K]
3 years ago
8

Which represents a quadratic function?

Mathematics
1 answer:
stiks02 [169]3 years ago
6 0
F(x)=x2 + 2x - 5 represents a quadratic function
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Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directric of x = -2?
vagabundo [1.1K]
Check the picture below.  So,the parabola looks like so, notice the distance "p". since the parabola is opening to the right, then "p" is positive, thus is 5.

\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
\boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})} \\\\
(x-{{ h}})^2=4{{ p}}(y-{{ k}}) \\
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\

\bf -------------------------------\\\\
\begin{cases}
h=3\\
k=1\\
p=5
\end{cases}\implies (y-1)^2=4(5)(x-3)\implies (y-1)^2=20(x-3)
\\\\\\
\cfrac{1}{20}(y-1)^2=x-3\implies \boxed{\cfrac{1}{20}(y-1)^2+3=x}

8 0
3 years ago
Read 2 more answers
What is the power notation of 125
loris [4]

Answer:

5³

Step-by-step explanation:

125 = 5 × 5 × 5 = 5³

8 0
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The bones of a mammal were discovered to have 3% as much Carbon-14 as they would have contained when
tankabanditka [31]
I be flexing 3 dollars carbon-144
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3 years ago
PLEASE HELP!! Compare & Contrast how Completing the Square is used to Convert a quadratic function to vertex form with how i
Likurg_2 [28]

Answer:

Step-by-step explanation:

Given a general quadratic formula given as ax²bx+c = 0

To generate the general formula to solve the quadratic equation, we can use the completing the square method as shown;

Step 1:

Bringing c to the other side

ax²+bx = -c

Dividing through by coefficient of x² which is 'a' will give:

x²+(b/a)x = -c/a

- Completing the square at the left hand side of the equation by adding the square of half the coefficient x i.e (b/2a)² and adding it to both sides of the equation we have:

x²+(b/a)x+(b/2a)² = -c/a+(b/2a)²

(x+b/2a)² = -c/a+(b/2a)²

(x+b/2a)² = -c/a + b²/4a²

- Taking the square root of both sides

√(x+b/2a)² = ±√-c/a + b²/√4a²

x+b/2a = ±√(-4ac+b²)/√4a²

x+b/2a =±√b²-4ac/2a

- Taking b/2a to the other side

x = -b/2a±√√b²-4ac/2a

Taking the LCM:

x = {-b±√b²-4ac}/2a

This gives the vertex form with how it is used to Solve a quadratic equation.

7 0
3 years ago
In the first quarter of 2010, U.S. advertisers spent $5.9 billion on online
Katyanochek1 [597]

Answer:

$1.4 B per year

Step-by-step explanation:

7 0
2 years ago
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