Answer:
y=-2.5[tex]x^{2}[/tex]+4.5x+1.5
Step-by-step explanation:
standard form of equation of parabola is,
y=a[tex]x^{2}[/tex]+bx+c
For x=0
1.5=0a+0b+c
1.5=c
For x=-2,
2.5=4a-2b+c
substituting the value of c
2.5=4a-2b+1.5
on solving,
4a-2b=1____________(1)
For x=4,
-60.5=16a+4b+c
substituting the value of c,
-60.5=16a+4b+1.5
on solving,
16a+4b=-62_______(2)
Multiplying equation 1 by 2,
8a-4b=2_______(3)
adding equation 2 and 3
16a+4b+8a-4b=-62+2
24a=-60
on solving,
a=-2.5
substituting the value of a in equation 1,
10-2b=1
2b=9
b=4.5
hence, equation of parabola in standard form is,
y=-2.5[tex]x^{2}[/tex]+4.5x+1.5
