Complete the square

Question 1

I mean i don’t rlly need to say anything i’ll just put workings lol

x^2+8x+17 in form (x+p)^2 +q

Answer 1

Which equals:
(x+4)^2 -16+17
= (x+4)^2 +1

Question 2

How do i get the coordinates of vertex of curve from that previous stuff?
(vertex = minimum point)

= (x+4)^2 +1

Answer 2

(x+4)^2 +1

(bracket must be 0)
x = -4

Sub into earlier equation = x^2+8x+17

-4^2+8(-4)+17 = 16-32+17 = 1

y = 1

Oh and also the 17 is where the line will end on the y axis so that’s pretty cool

Question 3

And how do u state the equation of line of symmetry from that previous stuff too?

Answer 3

x = -4?

I mean that’s what she wrote but its whatever

Question 4

How bout a harder question?

2x^2+4x+5 in form 2(x+p)^2 + q

Answer 4

Divide the 2 out from both x’s:

2(x^2+2x) +5

Complete the square within:

2[(x+1)^2 -1] +5

Time’s the 2 both bracket and that one number outside ig:

2(x+1)^2 -2 +5 then finishing touch:
2(x+1)^2 +3

Question 5

2x^2+4x+5 <– the curve’s equation

how u find coordinates of vertex?

Answer 5

We completed square giving us: 2(x+1)^2 +3

Bracket must = 0 so x = -1

Now just sub -1 into 2x^2+4x+5 for y
= 3

(-1, 3)

Question 6

2x^2+4x+5 <– the curve’s equation

How to sketch graph?

Answer 6

coordinates: (-1, 3)
completed square: 2(x+1)^2 -2 +5

The line is a smile and errr
- x is where the bottom of the line will be
- y is also where the bottom will be
- where the line meets is actually that +5 (that’s y coordinate)

Question 7

2x^2+4x+5 <– the curve’s equation

State the equation of line of symmetry…?

Answer 7

x = -1?

That’s literally what she wrote

Question 8

What do u do for a negative coefficient?

4-10x-x^2 in form p - (x+q)^2

Answer 8

Long story short, take the minus out (just like if there a number infront of x).
But here’s the long way anyway:

4-10x-x^2
-x^2-10x +4
-(x^2+10x) +4
-[(x+5)^2 -25] +4
-(x+5)^2 +25 +4
-(x+5)^2 +29

29- (x+5)^2