Answer:
a. [tex]y=x^2-3.8x-0.39[/tex]
b. [tex]y=x^2^ + 100[/tex]
c. [tex]y=x^2 + 4x + 5.5[/tex]
Step-by-step explanation:
Many different graphics can have the same vertex.
The equation of a parabola in the form of a vertex is:
[tex]y=a(x-h)^2+k[/tex]
where [tex](h,k)[/tex] is the vertex
[tex]h=1.9[/tex]
and
[tex]k=-4[/tex]
so the equation is:
[tex]y=a(x-1.9)^2+(-4)[/tex]
[tex]y=a(x-1.9)^2-4[/tex]
As we are not given the value of [tex]a[/tex], and we are only asked for an equation we can choose the value we like. I will choose a = 1 to simplify
[tex]y=(x-1.9)^2-4[/tex]
[tex]y=x^2-3.8x+3.61-4\\y=x^2-3.8x-0.39[/tex]
[tex]h=0[/tex]
and
[tex]k=100[/tex]
so the equation is:
[tex]y=a(x-0)^2 + 100[/tex]
[tex]y=ax^2+ 100[/tex]
again choosing a=1
[tex]y=x^2+100[/tex]
[tex]h=-2[/tex]
and
[tex]k=3/2[/tex]
so the equation is:
[tex]y=a(x-(-2))^2+3/2[/tex]
[tex]y=a(x+2)^2+3/2[/tex]
again choosing a=1
[tex]y=(x+2)^2+3/2[/tex]
[tex]y=x^2+4x+4+3/2\\y=x^2+4x+5.5[/tex]
