Quadratics?

Question

Quadratics
Note:
please help me!
and if you can explain too.
thank you!xD

1.y=(x+2)^2-5
2.y=-(x-4)^2+1
3.y=x^2+3
4.y=(x-1)^2-2
5.y=-2(x+5)^2-2
6.y=-1/2(x+4)^2+4
7.y=X^2-12x+36

Answer 1

First, get the quadratic in 'standard' form
ax² + bx + c
Then solve it using the quadratic formula
x = (-b ± √(b² - 4ac))/2a
(1)
(x+2)² - 5 = x² + 4x + 4 -5 = x² + 4x - 1
x = (-4 ± √(16 + 4))/2
x = .236
x = -.4.236

Now *you* do the rest of them so you'll understand how it works ☺

HTH

Doug

Answer 2

1. to create the solutions, imagine drawing a happy face.
the left eyebrow is x*x = x^2
the right eyebrow is 2*2 = 4
the nose is 2 * x = 2x
the big smile is x * 2 = 2x
when you add those components up, this is the equation.

(x+2)^2 - 5
= (x+2)(x+2) - 5
= x^2 + 2x + 2x + 4 - 5
= x^2 + 4x - 5
could also factored as
(x - 5)(x +1) = 0
so x = 5 or -1

Answer 3

1.)
(x + 2)^2 - 5
((x + 2) - sqrt(5))((x + 2) + sqrt(5))
(x + (2 - sqrt(5)))(x + (2 + sqrt(5)))

The x-intercepts are 2 - sqrt(5) and 2 + sqrt(5)

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2.)
-(x - 4)^2 + 1
-((x - 4)^2 - 1)
(x - 4)^2 - 1
((x - 4) + 1)((x - 4) - 1)
(x - 4 + 1)(x - 4 - 1)
(x - 3)(x - 5)

x-intercepts are 3 and 5

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3.)
x^2 + 3 = (x + isqrt(3))(x - isqrt(3))

x-intercepts are isqrt(3) and -isqrt(3)

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4.)
(x - 1)^2 - 2
((x - 1) + sqrt(2))((x - 1) - sqrt(2))
(x + (-1 + sqrt(2)))(x + (-1 - sqrt(2)))

x-intercepts are -1 + sqrt(2) and -1 - sqrt(2)

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5.)
-2(x + 5)^2 - 2
-2((x + 5)^2 + 1)
(x + 5)^2 + 1
((x + 5) - i)((x + 5) + i)
(x + (5 - i))(x + (5 + i))

x-intercepts are 5 - i and 5 + i

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6.)
(-1/2)(x + 4)^2 + 4
(-1/2)((x + 4)^2 - 8)
(x + 4)^2 - 8
((x + 4) - 2sqrt(2))((x + 4) + 2sqrt(2))
(x + (4 - 2sqrt(2)))(x + (4 + 2sqrt(2)))

x-intercepts are 4 - 2sqrtr(2) and 4 + 2sqrt(2)

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7.)
x^2 - 12x + 36 = (x - 6)^2

x-intercept is 6