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
[tex]y = (x - \frac{7}{2} )^{2} - \frac{9}{4}[/tex]
[tex](y + \frac{9}{4}) = (x - \frac{7}{2})^{2}[/tex]
So, this is an equation of parabola having vertex at [tex](\frac{7}{2}, -\frac{9}{4})[/tex] 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)
