Question

Can someone help me with four Algebra 2 questions?

Answer 1

1. Write the equation of the quadratic function with roots -10 and -8 and a vertex at (-9, -3).

2. Write the equation of the quadratic function with roots 0 and 1 and a vertex at (1/2, -2/3)

3. Write the equation of the quadratic function with roots -9 and and -3 and a vertex at (-6, -1).

4. Write the equation of the quadratic function with roots -2 and 4 and a vertex at (1, 9).

Answer 2

1. the quadratic equation is given by x^2-(a+b)X+ab
where a,b are the roots
since it is given that this passes through a point (x1,y1) your quadratic equation simply equated to y will be the answer

Answer 3

same procedure is applicable to all the 4
after writing the equation just verify it by giving x the value of x1

Answer 4

Would you mind telling me the answer for each one and explaining how you got it. I've got a final exam coming up and I'm trying to jot some things down.

Answer 5

in the first case roots are -10 and -8
then a=-10 b=-8
a+b=-18
ab=80
the quadratic expression is x^2-(-18)x+80
just equate this to y
therefore the equation is y=x^2+18x+80
given vertex is (-9,-3)
implies the above equation should satisfy for the given vertex values of x and y
implies x=-9 should fetch the value of y=-3
put x=-9
then y=(-9)^2+18(-9)+80 should fetch you -3 but the answer is -1 so just multiply both sides by 3
so your equation becomes y=3(x^2-18x+80)

Answer 6

Thank you... But what about the others?