Question

Can you match the graph to the equation and give a reason?

Answer 1

Equation A = Graph 3

Equation B = Graph 4

Equation C = Graph 1

Equation D = Graph 2

Explanation:

The first equation is y = x² - 7x + 10

This equation can be rearranged as

`y = (x - (7)/(2) )^(2) - (9)/(4)`

`(y + (9)/(4)) = (x - (7)/(2))^(2)`

So, this is an equation of parabola having vertex at
`((7)/(2), -(9)/(4))` 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)