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Here is a sketch of a curve.

YA
The equation of the curve is y = x2 + ax + b
where a and b are integers.
The points (0, -7) and (7, 0) lie on the curve.
Find the coordinates of the turning point of the curve.

Here is a sketch of a curve. YA The equation of the curve is y = x2 + ax + b where-example-1
User Shavkat
by
7.8k points

1 Answer

2 votes

Answer:

The turning point of the graph is at (3,-16)

Explanation:

The general equation of curve is given as:

y = x² + ax + b

The two point for which the equation satisfies is (0,-7) and (7,0).

Substitute (0,-7) in the general equation:

y = x² + ax + b

-7 = 0² + a(0) + b

b = -7

Substitute (7,0) in the general equation:

y = x² + ax + b

0 = 7² + 7a + b

Where b = -7

0 = 49 + 7a - 7

0 = 42 + 7a

a = -6

The equation of the curve is:

a = -6 and b = -7

y = x² + ax + b

y = x² - 6x - 7

Graph of the equation is attached below.

We can see that the the turning point of the graph is at (3,-16)

Here is a sketch of a curve. YA The equation of the curve is y = x2 + ax + b where-example-1
User JonathanBristow
by
8.4k points

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