Will give brainliest

a) solve 8x^2 - 14x + 5 = 0 by factoring and describe how your answers apply to the graph of 8x2 - 14x + 5 = 0.

b) write a quadratic that has x-intercepts of -2 and 1/3. show all of your steps.

(A) I start with writing out the factored form with the coefficients unknown:

We have now to figure out a,b,c, and d. I usually start with the constant term to see in which ways it could be obtained. Clearly, the constant 5 corresponds to the product bd. Well, 5 is prime so this product cannot be anything but 1*5 (or 5*1), so we already have a good choice for b and d:

then I try to see how we could get the -14 in front of x, while keeping an eye on the 8 in front of x^2. Given the b and d values, that can happen as follows: -14 = 5*(-2)+1*(-4), so

This is the factored form of the quadratic. So our equation is now

This makes solving the equation much easier. When is this product equal zero? When either of the factors equal zero!

So the solutions are 1/2 and 5/4.

What does this tell you about the graph? The solutions to the quadratic equation are the x-intercepts, so you know that the graph (which is a parabola) intercepts the x axis at 1/2 and also at 5/4.

(B) This is a similar problem but taken in reverse: we start out with known x-intercepts, or solutions to the quadratic, which we are to find. If the solutions are -2 and 1/3, then I can write them in a factored form:

(please verify for yourself that setting x to either -2 or 1/3 will result in 0)

Now multiply out:

which gives you the final quadratic with integer coefficients.

add an image

step-by-step explanation:

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation: