Given:
4 equations of quadratics function and the 4 sketches.
we will write the equation of each graph.
The first equation: y = x² - 6x + 8
We will find the roots of the function
y = (x- 4)(x - 2)
So, the function has 2 positive real roots x = 2, x = 4
so, it will be the function of the graph number 3
The second equation: y = (x - 6)(x + 8)
The function has 2 roots and the curve is opened up
The roots are x = 6, x = -8
The y-intercept = -48 (negative value)
So, it will be the function for the graph number 4
The third equation: y = (x-6)² + 8
The function has no real roots, this means there is no intersection between the function and the x-axis
so, the equation will be for the graph number 1
The fourth equation: y = -(x+8)(x-6)
Note: the leading coefficient is negative
So, the curve of the function is opened down
So, it will be the equation for the graph number 2