If f(x)=x^2+3x+5 what is f(3+h) ?

2 answers:

8 0

F(x) = x^2 + 3x + 5
f(3+h) = (3+h)^2 + 3(3+h) + 5 ... replace every x with 3+h
f(3+h) = (3+h)(3+h) + 3(3+h) + 5
f(3+h) = (3^2+2*3*h+h^2) + (3*3+3*h) + 5
f(3+h) = (9+6h+h^2) + (9+3h) + 5
f(3+h) = 9+6h+h^2 + 9+3h + 5
f(3+h) = h^2 + (6h+3h) + (9+9+5)
f(3+h) = h^2+9h+23

andriy [413]3 years ago

7 0

F(x)=x^2+3x+5
f(3+h)=(3+h)^2+3(3+h)+5
f(3+h)=9+6h+h^2+9+3h+5
f(3+h)=23+9h+h^2

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Make a table of values and create a line of best fit

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<h2>Explanation:</h2><h2></h2>

Hello! remember you have to write complete questions in order to get good and exact answers. Here I'll explain this in a general way assuming the following table:

$\begin{array}{cc}x & y\\0 & 0\\1 & 2\\2 & 4\\3 & 6\\4 & 8\\5 & 10\end{array}$

As you can see, x increases in steps of 1 units. So let's check the difference in y:

$\bullet \ \text{From x=0 to x=1} \\ \\ \Delta y=2-0=2 \\ \\ \\ \bullet \ \text{From x=1 to x=2} \\ \\ \Delta y=4-2=2 \\ \\ \\ \bullet \ \text{From x=2 to x=3} \\ \\ \Delta y=6-4=2 \\ \\ \\ \bullet \ \text{From x=3 to x=4} \\ \\ \Delta y=8-6=2 \\ \\ \\ \bullet \ \text{From x=4 to x=5} \\ \\ \Delta y=10-8=2$

So we have a constant difference and we can conclude the table represents a line. Since the line passes through then y is directly proportional to x, so we can write:

$y=kx \\ \\ Where: \\ \\ k \ is \ constant \ of \ proportionality \ or \ the \ slope$