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What are the x- and y-intercepts of the graph of y = x2 + 7x + 12?

Solution:

The x-intercepts of the curve can be determined by putting y = 0 and the y intercepts can be determined by putting x = 0 .

a) Determination of x intercepts

When we are determining the x-intercepts of the given function we are determining the zeroes of the function.

These are the values of x for which the y value will be zero. Therefore we have

⇒ x2 + 7x + 12 = 0

Factorising the left hand side we get,

⇒ x2 + 4x + 3x + 12 = 0

⇒ x(x + 4) + 3(x + 4) = 0

⇒ (x + 4)(x + 3) = 0

Therefore,

x + 4 = 0 ⇒ x = -4, The first x-intercept

x + 3 = 0 ⇒ x = -3, The second x – intercept

b) Determination of y – intercept

The y-intercept can be determined when x = 0. Therefore

y = (0)⇒ + 7(0) + 12 = 12

Therefore the y-intercept is 12.

The x – intercepts and y-intercept are depicted in the graph below:

What are the x- and y-intercepts of the graph of y = x2 + 7x + 12?

Summary:

The x- and y-intercepts of the graph of y = x2 + 7x + 12 are -3, -4 and 12 respectively.

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