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### Section 4-2 : Parabolas

For problems 1 – 7 sketch the graph of the following parabolas. The graph should contain the vertex, the y intercept, x-intercepts (if any) and at least one point on either side of the vertex.

1. $$f\left( x \right) = {\left( {x + 4} \right)^2} - 3$$ Solution
2. $$f\left( x \right) = 5{\left( {x - 1} \right)^2} - 20$$ Solution
3. $$f\left( x \right) = 3{x^2} + 7$$ Solution
4. $$f\left( x \right) = {x^2} + 12x + 11$$ Solution
5. $$f\left( x \right) = 2{x^2} - 12x + 26$$ Solution
6. $$f\left( x \right) = 4{x^2} - 4x + 1$$ Solution
7. $$f\left( x \right) = - 3{x^2} + 6x + 3$$ Solution

For problems 8 – 10 convert the following equations into the form $$y = a{\left( {x - h} \right)^2} + k$$.

1. $$f\left( x \right) = {x^2} - 24x + 157$$ Solution
2. $$f\left( x \right) = 6{x^2} + 12x + 3$$ Solution
3. $$f\left( x \right) = - {x^2} - 8x - 18$$ Solution