Answer:
y = 5(x - 3)² + 2
Step-by-step explanation:
y = a(x - h)² + k
y = a(x - 3)² + 2
7 = a(4 - 3)² + 2
a = 5
y = 5(x - 3)² + 2
The equation of the parabola is:
[tex]y = 5(x - 3)^2 + 2[/tex].
The equation of a parabola with vertex (h,k) is given by:
[tex]y = a(x - h)^2 + k[/tex]
In this problem, vertex (3,2), thus [tex]h = 3, k = 2[/tex], and:
[tex]y = a(x - 3)^2 + 2[/tex]
It contains point (4,7), which means that when [tex]x = 4, y = 7[/tex], and this is used to find a.
[tex]y = a(x - 3)^2 + 2[/tex]
[tex]7 = a(4 - 3)^2 + 2[/tex]
[tex]a + 2 = 7[/tex]
[tex]a = 5[/tex]
Thus, the equation is:
[tex]y = 5(x - 3)^2 + 2[/tex].
A similar problem is given at https://brainly.com/question/17987697
