Draw the graph of p (x)=x2-x-12 and find
its zeroes. Justify your answer.
Answers
EXPLANATION.
Graph of the Quadratic equation.
⇒ p(x) = x² - x - 12.
As we know that,
Factorizes the equation into middle term splits, we get.
⇒ y = x² - x - 12.
⇒ y = x² - 4x + 3x - 12.
⇒ y = x(x - 4) + 3(x - 4).
⇒ y = (x + 3)(x - 4).
Zeroes of the polynomials.
⇒ (x + 3)(x - 4) = 0.
⇒ x = -3 and x = 4.
When x = -3 then,
⇒ y = (-3)² - (-3) - 12.
⇒ y = 9 + 3 - 12.
⇒ y = 12 - 12.
⇒ y = 0.
Their Co-ordinates = (-3,0).
When x = 4 then,
⇒ y = (4)² - (4) - 12.
⇒ y = 16 - 4 - 12.
⇒ y = 16 - 16.
⇒ y = 0.
Their Co-ordinates = (4,0).
When x = 0 then,
⇒ y = (0)² - (0) - 12.
⇒ y = -12.
Their Co-ordinates = (0,-12).
Step-by-step explanation:
Given : Polynomial p(x)=x^2-x-12p(x)=x
2
−x−12 .
To find : The graph of the polynomial ?
Solution :
We plot the graph of polynomial on different value of x and y,
Since it is quadratic function it form a parabola.
The number of zeros are 2 and the zeros are the points where the graph of the polynomial intersects the x-axis.
Zeros are : (-3,0) and (4,0)
On y-axis the point is (0,-12).
The vertices of the parabola is (0.5,-12.25).
Refer the attached figure below.
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