You can solve for each variable (a, b, c) through forming a system of equations with each set of coordinates. You should have three equations after plugging in.
1. Plug in the coordinates for x and y into the general form. Remember y and f(x) represent the same quantity.
2. Simplify. (Remember the order of operations)
3. Repeat steps 1 & 2 for the other two points.
4. Take two equations at a time and eliminate one variable (c works well)
5. Then repeat using two equations and eliminate the same variable you eliminated in #4.
6. Take the two resulting equations and solve the system (you may use any method).
7. After finding two of the variables, select an equation to substitute the values back into.
8. Find the third variable.
9. Substitute a, b, and c back into the general equation.
write the equation of the parabola y=ax^2+bx+c that passes through the points(0,3), (1,4), and (2,3)
2 answers
since (0,3) and (2,3) have the same y-value, the vertex is at x=1. So, (1,4) is the vertex, and we have
y = a(x-1)^2 + 4
At x=0,
a(1)+4 = 3
a = -1
y = -(x-1)^2 + 4 = -x^2+2x+3
y = a(x-1)^2 + 4
At x=0,
a(1)+4 = 3
a = -1
y = -(x-1)^2 + 4 = -x^2+2x+3
1 answer