Answer:
y = (x + 1)(x - 7)
Step-by-step explanation:
The graphed quadratic function is an upward-opening parabola that crosses the x-axis at x = -1 and x = 7, and has a minimum point (vertex) at (3, -16).
The factored form of a quadratic function is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Factored form of a quadratic equation}}\\\\y=a(x-r_1)(x-r_2)\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$a$ is the leading coefficient}.\\\phantom{ww}\bullet\;\textsf{$r_1$ and $r_2$ are the $x$-intercepts (roots)}.\end{array}}[/tex]
Given that the x-intercepts are x = -1 and x = 7, then:
[tex]y=a(x-(-1))(x - 7)\\\\y=a(x+1)(x-7)[/tex]
To find the value of a, substitute the vertex (3, -16) into the equation:
[tex]-16=a(3+1)(3-7)\\\\\\-16=a(4)(-4)\\\\\\-16=-16a\\\\\\a=\dfrac{-16}{-16}\\\\\\a=1[/tex]
Therefore, the factored form of the graphed quadratic function is:
[tex]\Large\boxed{\boxed{y=(x+1)(x-7)}}[/tex]