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Answer:
<em>1. f(x)=−(x−3)(x+1) </em>
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<em>By multiplying the factors, the general form is f(x)= -x²+2x+3.</em>
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<em>Use the formula to find the vertex = (-b/2a, f(-b/2a)) , here in the above equation a=-1(As, a<0 the parabola is open downward), b=2. by putting the values.</em>
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<em>-b/2a = -2/2(-1) = 1</em>
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<em>f(-b/2a)= f(1)=-(1)²+2(1)+3= 4</em>
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<em>So, </em><em>Vertex = (1, 4)</em>
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<em>Now, find y- intercept put x=0 in the above equation. f(0)= 0+0+3, we get point</em><em> (0, 3).</em>
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<em>Now find x-intercept put y=0 in the above equation. 0= -x²+2x+3.</em>
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<em>-x²+2x+3=0 the factor form is already given in the question so, ⇒-(x-3)(x+1)=0 ⇒</em><em>x=3 , x=-1</em>
From vertex, y-intercept and x-intercept you can easily plot the graph of given parabolic equation. The graph is attached below.
