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padilas [110]
3 years ago
8

The graph of the quadratic function y = ax^2 + bx + c is given. Find a + b + c.

Mathematics
1 answer:
andrey2020 [161]3 years ago
4 0

Answer:

\frac{145}{24}\approx 6***

Answers may vary depending on the person reading the graph.

It is hard to tell what they think crosses nicely.

For example, I decided that the graph crossed nicely at the following points:

(0,3)

(2,8)

(6,5)

Step-by-step explanation:

I see that the graph crosses at (0,3),(2,8), and (6,5).

The equation y=ax^2+bx+c tells us the y-intercept is c since when x=0 we have y=a(0)^2+b(0)+c=0+0+c=c.

The y-intercept for our graph is 3. Therefore, c=3.

So far we have the equation:

y=ax^2+bx+3.

Let's enter the other points creating a system of linear equations to solve:

8=a(2)^2+b(2)+3

5=a(6)^2+b(6)+3

Let's simplify:

8=4a+2b+3

5=36a+6b+3

Let's subtract 3 on both sides:

5=4a+2b

2=36a+6b

I choose to solve the system by elimination.

Let's multiply the top equation by -3:

-15=-12a-6b

2=36a+6b

Now adding the equations results in:

-13=24a

Divide both sides by 24:

\frac{-13}{24}=a

Now using one of the equations we can find b:

5=4a+2b with a=\frac{-13}{24}

5=4\frac{-13}{24}+2b

5=\frac{-13}{6}+2b

Add 13/6 on both sides:

5+\frac{13}{6}=2b

\frac{30+13}{6}=2b

\frac{43}{6}=2b

Divide both sides by 2:

\frac{43}{2(6)}=b

\frac{43}{12}=b

So we have the equation:

y=\frac{-13}{24}x^2+\frac{43}{12}+3

Let's evaluate a+b+c now:

\frac{-13}{24}+\frac{43}{12}+3

\frac{-13+86+72}{24}

\frac{73+72}{24}

\frac{145}{24}

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