Respuesta :
Answer:
a. [tex]y=5(x-100)^2+200[/tex]
b. [tex]y=-2(x+\frac{3}{4})^2-6[/tex]
Step-by-step explanation:
the equation of a quadratic function in the vertex form is:
[tex]y=a(x-h)^2+k[/tex]
where [tex]a[/tex] is the leading coefficient, and [tex](h,k)[/tex] is the vertex.
- for a:
we have the vertex [tex](100,200)[/tex] so [tex]h=100[/tex] and [tex]k=200[/tex], thus the equation is:
[tex]y=a(x-100)^2+200[/tex]
and you can choose any value for [tex]a[/tex] other than 1. I will choose 5:
[tex]y=5(x-100)^2+200[/tex]
- for b:
we have the vertex [tex](\frac{-3}{4}, -6)[/tex] so [tex]h=\frac{-3}{4}[/tex] and [tex]k=-6[/tex], thus the equation is:
[tex]y=a(x-(-\frac{3}{4}))^2+(-6)[/tex]
[tex]y=a(x+\frac{3}{4})^2-6[/tex]
and you can choose any value for [tex]a[/tex] other than 1. I will choose -2 this time:
[tex]y=-2(x+\frac{3}{4})^2-6[/tex]
