Fungsi Kuadrat
Fungsi Kuadrat
Soal !!!
1. y = x^2- 25
2. y = -x^2 + 7x -12
3. y = - x^2 – 8x +
9
4. y = -2x^2– 7x + 4
5. y = -x^2 + 6x
Penyelesaian
1. y =x^2– 25
y = 0
0 =x^2– 25
(x – 5)(x + 5)
x = 5 x + 5
(5,0)(-5,0)
x = 0
y = 0^2 – 25
y = -25
(0,25)
Xp = - (b/2a)
= -
(0/2.1)
= 0
Yp = -(b^2-
4ac/4a)
= -(0^2-
4.1 -25/4.1)
= -(0 +
100/4
= -25
(0,-25)
2. y = -x^2 + 7x – 12
y = 0
0 = x^2 + 7x – 12
(-x + 4)(x – 3)
x = 4 x = 3
(4,0)(3,0)
x = 0
y = 0^2 + 7(0) – 12
y = -12
(0,12)
Xp = -(b/2a)
=
-(7/2.1)
= -(7/-2)
= 3,5
Yp = -(b^2 –
4ac/4a)
= -b^2 -
4,-1,-12/4,-1)
= -(49
– 48/-4)
=
-(1/-4)
= 0,25
(3,5; 0,25)
3.
y
= –x^2 – 8x + 9
y
= 0
0 = -x^2 – 8x + 9
(-x
– 9) (x – 1)
x
= -9 x = 1
(-9,
0) (1, 0)
x
= 0
y
= -0^2 -8(0) + 9
y
= 9
(0,
9)
Xp = -(b/2a)
=
-(-8/2.(-1))
=
-4
Yp = -(b^2 – 4ac/4a)
=
-(-8^2 – 4(-1).9)/4(-1))
=
-(64 + 36/-4)
=
- (-25)
=
25
(-4,
25)
4.
y = 0
(0,5; 0) (-4, 0)
x = 0
y = -2.0^2 – 7.0 + 4
y = 4
Xp =
-(b/2a)
= -(-7/2.-2)
=-(-7/-4)
= - 1,75
Yp =
-(b^2 – 4ac/4a)
=-
(7^2 – 4.-2.4/4.-2)
=
-(49 + 32/-8)
=
-(-10,125)
=
10,125
(-1,75;
10,125)
5.
y
= -x^2 + 6x
y
= 0
-x^2
+ 6x
x(-x
+ 6) = 0
x
= 0 x = 6
(0,
0) (6,0)
x
= 0
y
= 0^2 + 6(0)
y
= 0
(0, 0)
Xp = -(b/2a)
=
-(6/2.-1)
=
-(-3)
=
3
Yp = -(b^2 – 4ac/4a)
=
-(6^2 – 4.-1.0/4(-1))
=
-(36 – 0/-4)
=
-(-9)
= 9
(3,
9)
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