SOLUTION: a porabola has a y intercept of -4 and passes thru points (-2,8) and (1,-2). determine the equation of the porabola in standard form. remember standard for is y = ax2 + bx + c.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: a porabola has a y intercept of -4 and passes thru points (-2,8) and (1,-2). determine the equation of the porabola in standard form. remember standard for is y = ax2 + bx + c.       Log On


   

Question 1062085: a porabola has a y intercept of -4 and passes thru points (-2,8) and (1,-2). determine the equation of the porabola in standard form. remember standard for is y = ax2 + bx + c.
Found 2 solutions by josmiceli, josgarithmetic:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The y-intercept occurs where +x+=+0+, so
the y-intercept is +y%280%29+
+y%280%29+=+a%2A0%5E2+%2B+b%2A0+%2B+c+
+y%280%29+=+c+
+c+=+-4+
------------------
( -2,8 )
+y+=+a%2Ax%5E2+%2B+b%2Ax+-+4+
+8+=+a%2A%28-2%29%5E2+%2B+b%2A%28-2%29+-+4+
+8+=+4a+-+2b+-+4+
+4a+-+2b+=+12+
(1) +2a+-+b+=+6+
------------------------------
( 1, -2 )
+y+=+a%2Ax%5E2+%2B+b%2Ax+-+4+
+-2+=+a%2A1%5E2+%2B+b%2A1+-+4+
+-2+=+a+%2B+b+-+4+
(2) +a+%2B+b+=+2+
------------------------------
Add (1) and (2)
(1) +2a+-+b+=+6+
(2) +a+%2B+b+=+2+
-------------------
+3a+=+8+
+a+=+8%2F3+
and
(2) +a+%2B+b+=+2+
(2) +8%2F3+%2B+b+=+2+
(2) +b+=+6%2F3+-+8%2F3+
(2) +b+=+-2%2F3+
-------------------------
The equation is:
+y+=+%288%2F3%29%2Ax%5E2+-+%282%2F3%29%2Ax+-+4+
-------------------------------
check:
( -2,8 )
+y+=+%288%2F3%29%2Ax%5E2+-+%282%2F3%29%2Ax+-+4+
+8+=+%288%2F3%29%2A%28-2%29%5E2+-+%282%2F3%29%2A%28-2%29+-+4+
+24+=+8%2A4+%2B+4+-+12+
+24+=+32+-+8+
+24+=+24+
OK
------------------
(1,-2)
+y+=+%288%2F3%29%2Ax%5E2+-+%282%2F3%29%2Ax+-+4+
+-2+=+%288%2F3%29%2A1%5E2+-+%282%2F3%29%2A1+-+4+
+-2+=+8%2F3+-+2%2F3+-+4+
+-6+=+8+-+2+-+12+
+-6+=+8+-+14+
+-6+=+-6+
OK


Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The first point described is (0,-4).
a%2A0%5E2%2Bb%2A0%2Bc=-4
highlight_green%28c=-4%29

Next two points give equations system%28a%2A%28-2%29%5E2%2Bb%28-2%29-4=8%2Ca%2A1%5E2%2Bb%281%29-4=-2%29

system%284a-2b=12%2Ca%2Bb=2%29

system%282a-b=6%2Ca%2Bb=2%29---------and this system of LINEAR equations in variables a and b should be easy to solve.

You should now be able to solve for a and b, and your form as y=ax^2+bx+c is GENERAl FORM, not "standard form".