draw the graph of polynomial f(x)=x^2+2x-3
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EXPLANATION.
Graph of the polynomial.
⇒ f(x) = x² + 2x - 3.
As we know that,
⇒ y = x² + 2x - 3.
Factorizes the equation into middle term splits, we get.
⇒ y = x² + 3x - x - 3.
⇒ y = x(x + 3) - 1(x + 3).
⇒ y = (x - 1)(x + 3).
Zeroes of the equation.
⇒ (x - 1)(x + 3) = 0.
⇒ x = 1 and x = - 3.
Put the value of x = 1 in the equation, we get.
⇒ y = x² + 2x - 3.
⇒ y = (1)² + 2(1) - 3.
⇒ y = 1 + 2 - 3.
⇒ y = 3 - 3.
⇒ y = 0.
Their Co-ordinates = (1,0).
Put the value of x = - 3 in the equation, we get.
⇒ y = x² + 2x - 3.
⇒ y = (-3)² + 2(-3) - 3.
⇒ y = 9 - 6 - 3.
⇒ y = 9 - 9.
⇒ y = 0.
Their Co-ordinates = (-3,0).
Put the value of x = 0 in the equation, we get.
⇒ y = x² + 2x - 3.
⇒ y = (0)² + 2(0) - 3.
⇒ y = 0 + 0 - 3.
⇒ y = - 3.
Their Co-ordinates = (0,-3).
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