SOLUTION: If the quadratic equation f(x)=x^2+2x-2 were translated up 5 units and to the right 4 units, then what would be the zeros of the resulting quadratic function? Explain your solution

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Question 570987: If the quadratic equation f(x)=x^2+2x-2 were translated up 5 units and to the right 4 units, then what would be the zeros of the resulting quadratic function? Explain your solution.
Answer by lwsshak3(6463) (Show Source):
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If the quadratic equation f(x)=x^2+2x-2 were translated up 5 units and to the right 4 units, then what would be the zeros of the resulting quadratic function? Explain your solution.
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Translating a function up or down is graphically in effect moving the entire curve up or down, that is, f(x) goes up or down. In this case, moving f(x) 5 unit up looks like this: f(x)+5=(x^2+2x-2)+5.
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Translating a function right or left is moving the entire curve left or right. In this case moving the curve 4 units to the right means adding -4 units to x like this:f(x)= (x-4)^2+2(x-4)-2
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Translating the function 5 units up and 4 units to the right look like this:
f(x)=(x-4)^2+2(x-4)-2+5
solving for zeros
f(x)=x^2-8x+16+2x-8-2+5
f(x)=x^2-6x+11
discriminant=b^2-4ac=36-4*1*11<0
Therefore, translated function has no real roots or zeros.