A quadratic function f(x)=5x2+30x+4.
a.) Find the quadratic function in standard form.
f(x)=5x2+30x+4f(x)=5(x2+6x)+4Factor out 5 from the x-termf(x)=5(x2+6x+9)+4−(5)(9)Complete the square: add 9 inside the parentheses, subtract (5)(9) outsidef(x)=5(x+3)−41Factor and simplify
The standard form is f(x)=5(x+3)−41.
b.) Draw its graph.
c.) Find its maximum or minimum value.
Based from the graph in part (b), since the graph opens upward the minimum value of f is f(−3)=−41.
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