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Complete the square to rewrite y = x2 + 8x – 4 in vertex form, and then identify the minimum y-value of the function

babunello [35]

Answer:

The vertex form is (x + 4)² - 20

The minimum value of the function is -20

Step-by-step explanation:

* Lets write the general form and the vertex form of the

quadratic function

- General form ⇒ ax² + bx + c, where a , b , c are constant

- Vertex form ⇒g(x - h)² + k, where g , h , k are constant and

(h , k) is the vertex point (minimum or maximum)

- By equating them we can find the vertex point

* Lets do that in the problem

∵ y = x² + 8x - 4

∴ x² + 8x - 4 = g(x - h)² + k ⇒ solve the bracket

∴ x² + 8x - 4 = g(x² - 2xh + h²) + k ⇒ open the bracket

∴ x² + 8x - 4 = gx² - 2ghx + gh² + k

* Now lets equate the like terms

- Let x² = gx²

∴ g = 1

- Let 8x = -2ghx ⇒ -2gh = 8 ⇒ -2(1)h = 8 ⇒ -2h = 8 ⇒ ÷ -2 for both sides

∴ h = -4

- let -4 = gh² + k ⇒ -4 = (1)(-4)² + k ⇒ 16 + k = -4 ⇒ -16 for both sides

∴ k = -4 - 16 = -20

* Substitute these values in the equation

∴ x² + 8x - 4 = (x - -4)² + -20

* The vertex form is (x + 4)² - 20

∵ The vertex point is (h , k)

∴ The vertex point is (-4 , -20)

* The minimum value of the function is the value of y

of the vertex point

∴ The minimum value of the function is -20

6 0

3 years ago

Read 2 more answers

Dropping less than two inches per mile after emerging from the mountains 3trillion gallons could supply all of country A’s house

Viefleur [7K]

Answer:

What is your answer?

Step-by-step explanation:

3 0

3 years ago

What is the expand form for 0.632

pav-90 [236]

0.600 is ur answer Hopes this helps u.

5 0

4 years ago

What value of x is in the solution set of 2x – 3 > 11 – 5x?

Alla [95]

2x-3>11-5x

Simplify both sides of the equation

2x-3>-5x+11

Add 5x to both sides

2x-3+5x>-5x+11+5x

7x-3>11

Add 3 to both sides

7x-3+3>11+3

7x>14

Divide both sides by 7

7x/7>14/7

x>2

I hope that's help !

5 0

3 years ago

Read 2 more answers

The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is . What is the standard form of the

kvasek [131]

Answer:

Point-Slope form: $y+1=-\frac{6}{15}(x+5)\\$

standard form: $2x+5y=-15$

Step-by-step explanation:

The standard form is given by: $Ax+By=C$

The point-slope form is given by: $y-y_1=m(x-x_1)$

Let's call $(-5,-1)$ as point $(x_1,y_1)$ , and

point $(10,-7)$ as point $(x_2,y_2)$

We also know that the slope $m$ is given by $m=\frac{y_2-y_1}{x_2-x_1}$

Let's find the slope:

$m=\frac{-7-(-1)}{10-(-5)}=-\frac{6}{15}$

1. So, point slope form can be written as:

$y-(-1)=-\frac{6}{15}(x-(-5))\\y+1=-\frac{6}{15}(x+5)\\$

2. Rearranging this equation and bringing all x's and y's to one side and the number to another side will give us the standard form. So:

$y+1=-\frac{6}{15}x-2\\y+\frac{6}{15}x=-2-1\\y+\frac{6}{15}x=-3$

But A, B, and C (standard form) needs to be integers, so to get rid of the denominator , we multiply the whole equation by 15. So we have:

$y+\frac{6}{15}x=-3\\15y+6x=-45$

We can factor out a 3, so it becomes:

$15y+6x=-45\\5y+2x=-15$

So standard form is $2x+5y=-15$

8 0

4 years ago

I need Help I don't understand ​

I need Help I don't understand