Respuesta :
Given:
Consider the quadratic function is
[tex]y=a(x-h)^2+k[/tex]
With given vertex (5,8) and given point (1,3).
To find:
The equation of quadratic function.
Solution:
The quadratic function is
[tex]y=a(x-h)^2+k[/tex] ...(i)
Where, (h,k) is the vertex and a is a constant.
Vertex is (5,8). So,
[tex](5,8)=(h,k)[/tex]
[tex]h=5,k=8[/tex]
Putting [tex]h=5,k=8[/tex] in (i), we get
[tex]y=a(x-5)^2+8[/tex] ...(ii)
The given point is (1,3). Putting x=1 and y=3 in (ii), we get
[tex]3=a(1-5)^2+8[/tex]
[tex]3-8=a(-4)^2[/tex]
[tex]-5=16a[/tex]
[tex]-\dfrac{5}{16}=a[/tex]
Putting [tex]a=-\dfrac{5}{16}[/tex] in (ii), we get
[tex]y=-\dfrac{5}{16}(x-5)^2+8[/tex]
Therefore, the required quadratic function is [tex]y=-\dfrac{5}{16}(x-5)^2+8[/tex].
