Respuesta :
We can write the equation of a parabola in to forms.
The standard form:
[tex]y=ax^2+bx+c[/tex]Or the vertex form:
[tex]y=a(x-h)^2+k[/tex]Where the point (h,k) is the vertex. We are going to use this one to solve this problem.
We have that the vertex coordinates are (2,7), so h=2 and k=7. So we have the formula:
[tex]y=a(x-2)^2+7[/tex]We just need to find a. For this we use the second point given (4,2). Replace x=4 and y=2 in the formula ans solve for a:
[tex]2=a(4-2)^2+7[/tex][tex]2-7=a(2)^2[/tex][tex]-5=4a[/tex][tex]a=-\frac{5}{4}[/tex]Then we have the complete equation for the given parabola:
[tex]y=-\frac{5}{4}(x-2)^2+7[/tex]To write it in the standard form we just have to use the binomial squared fomula:
[tex]y=-\frac{5}{4}(x^2-4x+4)^{}+7[/tex][tex]y=-\frac{5}{4}x^2+5x-5^{}+7[/tex][tex]y=-\frac{5}{4}x^2+5x+2[/tex]And in the standard form a = -5/4, b=5 and c=2
