Answer:
Equation A = Graph 3
Equation B = Graph 4
Equation C = Graph 1
Equation D = Graph 2
Step-by-step explanation:
The first equation is y = x² - 7x + 10
This equation can be rearranged as
![y = (x - \frac{7}{2} )^{2} - \frac{9}{4}](https://tex.z-dn.net/?f=y%20%3D%20%28x%20-%20%5Cfrac%7B7%7D%7B2%7D%20%29%5E%7B2%7D%20-%20%5Cfrac%7B9%7D%7B4%7D)
![(y + \frac{9}{4}) = (x - \frac{7}{2})^{2}](https://tex.z-dn.net/?f=%28y%20%2B%20%5Cfrac%7B9%7D%7B4%7D%29%20%3D%20%28x%20-%20%5Cfrac%7B7%7D%7B2%7D%29%5E%7B2%7D)
So, this is an equation of parabola having vertex at
and the axis is parallel to positive y-axis.
Therefore, graph 3 is correct for this equation A.
The second equation is y = (x - 4)(x + 2)
⇒ y = x² - 2x - 8 = (x - 1)² - 9
⇒ y + 9 = (x - 1)²
So,this is an equation of parabola, having vertex at (1,-9) and axis is parallel to positive y-axis.
Therefore, graph 4 is correct for this equation B.
Now, in equation C, y = (x - 4)² + 2, ⇒ y - 2 = (x - 4)²
This is also an equation of parabola having vertex at (4,2) and the axis is parallel to positive y-axis.
Therefore, graph 1 is correct for this equation C.
Now, the remaining equation D is of graph 2.
(Answer)