Quadratics, SMB-015

The diagram shows the curve with equation `y = x^2-7x + 10`. The curve intersects the `x`-axis at points `A and B`. The point `C` on the curve has the same `y`-coordinate as the `y`-intercept of the curve.

Find the `x`-coordinates of points `A and B.` (2 marks)

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Write down the coordinates of `C.` (2 marks)

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Show Answers Only

`A = 2,\ \ B = 5`
`(7, 10)`

Show Worked Solution

i. `y`	`= x^2-7x + 10`
	`= (x-2) (x-5)`

`:.x = 2 or 5`

`:.\ \ x text(-coordinate of)\ \ A = 2`

`x text(-coordinate of)\ \ B = 5`

ii. `y\ text(intercept occurs when)\ \ x = 0`

`=>y text(-intercept) = 10`

`C\ text(occurs at intercept:)`

`y`	`= x^2-7x + 10`	`\ \ \ \ \ text{… (1)}`
`y`	`= 10`	`\ \ \ \ \ text{… (2)}`

`(1) = (2)`

`x^2-7x + 10`	`= 10`
`x^2-7x`	`= 10`
`x (x-7)`	`= 10`

`x = 0 or 7`

`:.\ C\ \ text(is)\ \ (7, 10)`