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4 years ago

The equation f(x) = 3x2 − 24x + 8 represents a parabola. What is the vertex of the parabola?

1 answer:

s2008m [1.1K]4 years ago

5 0

$\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{-24}x\stackrel{\stackrel{c}{\downarrow }}{+8} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{-24}{2(3)}~~,~~8-\cfrac{(-24)^2}{4(3)} \right)\implies (4~~,~~8-48)\implies (4~~,~-40)$

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The size of a TV is measured by its diagonal. You want to buy a TV that has a 32

ANEK [815]

The width of the TV is 27.9 inches

Step-by-step explanation:

Given,

Diagonal of TV = 32 inch

Height of TV = 15.7 inch

The diagonal makes the TV into a right triangle,

Therefore,

Diagonal = hypotenuse = c = 32 inch

Height = perpendicular = a = 15.7 inch

Width = base = b

Using pythagoras theorem

$a^2+b^2=c^2\\(15.7)^2+b^2=(32)^2\\246.49+b^2=1024\\b^2=1024-246.49\\b^2=777.51$

Taking square root on both sides

$\sqrt{b^2}=\sqrt{777.51}\\b=27.88$

Rounding off to nearest tenth

b = 27.9 inches

The width of the TV is 27.9 inches

Keywords: Pythagoras theorem, square root

Learn more about square root at:

#LearnwithBrainly

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3 years ago

Triangle DEF has coordinates D(3, 4), E(4, 1), and F(1, -2). If the triangle is

fenix001 [56]

Answer:

Hello! answer: coordinates of E' are (16, 4)

Step-by-step explanation:

4 × 4 = 16 4 × 1 = 4 therefore the new coordinates are (16, 4)

5 0

3 years ago

32+44 distributive property

n200080 [17]

Answer: 76

Step-by-step explanation:

30 + 40 = 70

4 + 2 = 6

70 + 6 = 76

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3 years ago

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Feliz [49]

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4 years ago

Find quadratic polynomial which best fits the function f(x)=e^x and x=0, in the sense that g(0)= f(0), and g'(0) = f'(0), and g"

Dmitriy789 [7]

Let $g(x)=ax^2+bx+c$ . Then

$\begin{cases}g(0)=c\\g'(0)=b\\g''(0)=2a\end{cases}$

Meanwhile, since $f(x)=e^x$ , you have $f(0)=f'(0)=f''(0)=e^0=1$ .

It follows that $a=\dfrac12$ , $b=1$ , and $c=1$ , so that the quadratic fit for $f(x)=e^x$ that satisfies the given points is

$g(x)=\dfrac12x^2+x+1$

Note that this is just the second-order Taylor polynomial for $e^x$ about $x=0$ .

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4 years ago