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1 year ago

A portion of the Quadratic Formula proof is shown. Fill in the missing reason.

Mathematics

1 answer:

katrin [286]1 year ago

6 0

The quadratic equation ax²+bx+c = 0 is given and this is illustrated below.

<h3>How to illustrate the equation?</h3>

ax²+bx+c = 0

Step 1: Subtract c from both sides

ax²+bx+c-c = 0-c

ax²+bx = -c

Step 2: Divide both sides of the equation by a

ax²/a + bx/a = -c/a

x² + bx/a = -c/a

Step 3: Complete the square and add the quantity (b/2a)² times a squared to both sides

x² + bx/a + (b/2a)² = -c/a + (b/2a)²

Step 4: Square the quantity b/2a on the right side of the equation

x² + bx/a + (b/2a)² = -c/a + b²/4a²

Step 5: Find a common denominator on the right side of the equation which is 4a²

x² + bx/a + (b/2a)² = -4ac/4a² + b²/4a²

Step 6: Add the fractions together on the right side of the equation

x² + bx/a + (b/2a)² = (-4ac+ b²)/4a²

Step 7: The equation on the left is to be written as a perfect square as shown

(x+b/2a)² = (-4ac+ b²)/4a²

Step 8: Take the square root of both sides

√(x+b/2a)² = √ (-4ac+ b²)/4a²

(x+b/2a) = √(-4ac+ b²)/2a

Step 9: subtract b/2a from both sides

x+b/2a - b/2a = -b/2a + √(-4ac+ b²)/2a

x = -b/2a + √(-4ac+ b²)/2a

Step 10: Add the fractions together on the right-hand side

x = -b±√(-4ac+ b²)/2a

This will then gives the required equation.

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The midpoint of \overline{\text{AB}}

Schach [20]

Answer:

<em>The coordinates of b are: B=(-7,-8)</em>

Step-by-step explanation:

We are given the coordinates of the midpoint of $\overline{\text{AB}}$ as M=(-5,-2).

We are also given the coordinates of A=(-3,4). The question requires us to calculate the coordinates of the other endpoint B.

Let (xb,yb) the coordinates of B. The coordinates of the midpoint can be calculated as follows:

$\displaystyle x_m=\frac{x_a+x_b}{2}$

$\displaystyle y_m=\frac{y_a+y_b}{2}$

We know xa=-3 and xm=-5. Solve the first equation for xb:

$2x_m=x_a+x_b\Rightarrow x_b=2x_m-x_a$

Substituting:

$x_b=2\cdot (-5)-(-3)=-10+3$

$x_b=-7$

We can solve the second equation for xb and get:

$y_b=2y_m-y_a$

Since ya=4 and ym=-2, then:

$y_b=2\cdot (-2)-(4)=-4-4$

$y_b=-8$

Thus, the coordinates of b are: B=(-7,-8)

4 0

3 years ago

Complete the square to re-write the quadratic function in vertex form: y=x2-x+3

Anna [14]

Answer:

Step-by-step explanation:

hello :

note : the vertex form is :

ax²+bx+c = a(x+(b)/(2a))²- delta/4a² and delta = b²- 4ac

in this exercice you have : a =1 b = -1 and c= 3

continu ..........

5 0

2 years ago

Suppose that f(x) is an EVEN function and let the integral f(x) dx from 0 to 1=5 and the integral f(x) dx from 0 to 7 =1. What i

Cerrena [4.2K]

<span>Since it's even, the integral from -7 to -1 is the same as the integral from 1 to 7.
</span><span>think about
x^2 from 0..1,its 1/3
from 0..7 its 7^3/3
from -1..7 its 7^3/3+1/3
</span>
<span>from -7..-1 of x^2 its -1/3+7^3/3 to get this without integrating we just do 7^3/3-1/3 which is the integral from 0..7 minus the integral from 0..1
</span><span>So the integral from 1 to 0 f(x) dx = 5 changes to the integral from 0 to 1 f(x) dx = -5 and you add it to the integral from 0 to 7 which is 1 making -4</span>

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3 years ago

Write and solve the equation. Show all work.

ozzi

Answer:

Step-by-step explanation:

57 - 3 = 54. 54/2 = 27.

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3 years ago

10tu^3 + 4v - 3v<br><br> must combine like terms solve or rewrite expression

pshichka [43]

10tu³ + v is the simplified form.

<h3>What is algebraic expression?</h3>

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