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3 years ago

Which function in vertex form is equivalent to f(x) = 4 + x2 – 2x?

Mathematics

1 answer:

blondinia [14]3 years ago

9 0

X^2 - 2x + 4
= (x - 1)^2 - 1 + 4
= (x - 1)^2 + 3

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Find the coordinates of the midpoint of a segment with the given endpoints.

Arada [10]

1. x midpoint: (-9+4)/(2) = -2
2. y midpoint: (3+7)/(2) = 5
3. The midpoint is (-2,5)

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2 years ago

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Solve this equation for x: 2x^2 + 12x - 7 = 0

zhannawk [14.2K]

Answer:

x=0.5355 or x=-6.5355

First step is to: Isolate the constant term by adding 7 to both sides

Step-by-step explanation:

We want to solve this equation: $2x^2 + 12x - 7 = 0$

On observation, the trinomial is not factorizable so we use the Completing the square method.

Step 1: Isolate the constant term by adding 7 to both sides

$2x^2 + 12x - 7+7 = 0+7\\2x^2 + 12x=7$

Step 2: Divide the equation all through by the coefficient of $x^2$ which is 2.

$x^2 + 6x=\frac{7}{2}$

Step 3: Divide the coefficient of x by 2, square it and add it to both sides.

Coefficient of x=6

Divided by 2=3

Square of 3= $3^2$

Therefore, we have:

$x^2 + 6x+3^2=\frac{7}{2}+3^2$

Step 4: Write the Left Hand side in the form $(x+k)^2$

$(x+3)^2=\frac{7}{2}+3^2\\(x+3)^2=12.5\\$

Step 5: Take the square root of both sides and solve for x

$x+3=\pm\sqrt{12.5}\\x=-3\pm \sqrt{12.5}\\x=-3+ \sqrt{12.5}, $ or $x= -3- \sqrt{12.5}\\$x=0.5355 or x=-6.5355$

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2 years ago

How do you estimate 2,641 x 9

ASHA 777 [7]

To estimate 2641 x 9 is that you round each number. so it would be 2641 to 2640 and the 9 would round to 10. 2640 x 10

3 0

2 years ago

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Is 3x^2 + x^2 equal to

wariber [46]

The answer is a)3x^4

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2 years ago

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Solve the following system of equations. What is one x-value of a solution?

gulaghasi [49]

Answer:

There is some mistake in the question, because the solutions are x = -1.445 and x = -34.555

Step-by-step explanation:

Given the functions:

f(x) = x² + 4x + 10

g(x) = -32x - 40

we want to find the points at which f(x) = g(x).

x² + 4x + 10 = -32x - 40

x² + 4x + 10 + 32x + 40 = 0

x² + 36x + 50 = 0

Using quadratic formula:

$x = \frac{-b \pm \sqrt{b^2-4(a)(c)}}{2(a)}$

$x = \frac{-36 \pm \sqrt{36^2-4(1)(50)}}{2(1)}$

$x = \frac{-36 \pm 33.11}{2}$

$x_1 = \frac{-36 + 33.11}{2}$

$x_1 = -1.445$

$x_2 = \frac{-36 - 33.11}{2}$

$x_2 = -34.555$

5 0

2 years ago