Kerjakanlah soal berikut dengan baik dan benar
Jawaban nomor 2 sampai 4 ada digambar
Jawaban:
1) menentukan sumbu simetri
a) f(x)= x²-6x+5
b) f(x)= 5-4x-x²
penyelesaian:
rumus sumbu simetri x= -b/2a
a) f(x)= x²-6x+5 › a=1, b=–6, c=5
x= -b/2a
= –(–6)/2.1
= 6/2
= 3
b) f(x)= 5–4x–x² › a=–1, b=–4, c= 5
x= -b/2a
= –(–4)/2.(–1)
= 4/–2
= –2
2) menentukan nilai optimum
a) y= x²-2x-8
b) y= 16-6x-x²
penyelesaian:
rumus nilai optimum y= -(b²-4ac)/4a
a) y= x²-2x-8 › a=1, b=–2, c=–8
= -b²-4ac/4a
= –((–2)²-4.1.(–8))/4.1
= –(4+32)/4
= –36/4
= –9
b) y= 16–6x–x² › a=–1, b=–6, c=16
= -b²-4ac/4a
= –(–6)²-4(–1).16)/4(–1)
= –(36+64)/–4
= 100/4
= 25
3) menentukan koordinat titik puncak
rumus titik puncak (xp,yp)
a) f(x)= 8-2x-x²
penyelesaian:
f(x)= 8–2x–x² › a=–1, b=–2, c=8
xp= -b/2a
= –(–2)/2(–1)
= 2/–2
=–1
yp= -b²-4ac/4a
= –((–2)²–4(–1).8/4(–1))
= –(4+32)/–4
= 36/4
= 9