Given three points on a parabola, (P(0, 0)), (Q(1, 1)), and (R(2, 4)), find the equation of the parabola.

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Accepted Answer

Step:1 ：Step 1: A standard form of the equation of a parabola is (y = ax^2 + bx + c). We can substitute the given points into this equation to form a system of equations.Step:2 ：Step 2: Substituting (P(0, 0)) into the equation, we get (0 = a*0^2 + b*0 + c), which simplifies to (c = 0).Step:3 ：Step 3: Substituting (Q(1, 1)) into the equation, we get (1 = a*1^2 + b*1 + 0), which simplifies to (a + b = 1).Step:4 ：Step 4: Substituting (R(2, 4)) into the equation, we get (4 = a*2^2 + b*2 + 0), which simplifies to (4a + 2b = 4).Step:5 ：Step 5: Solving the system of equations (begin{cases} a + b = 1 4a + 2b = 4end{cases}) we find that (a = 1) and (b = 0).

Answer

Step: 1 ：Step 1: A standard form of the equation of a parabola is (y = ax^2 + bx + c). We can substitute the given points into this equation to form a system of equations.Step: 2 ：Step 2: Substituting (P(0, 0)) into the equation, we get (0 = a*0^2 + b*0 + c), which simplifies to (c = 0).Step: 3 ：Step 3: Substituting (Q(1, 1)) into the equation, we get (1 = a*1^2 + b*1 + 0), which simplifies to (a + b = 1).Step: 4 ：Step 4: Substituting (R(2, 4)) into the equation, we get (4 = a*2^2 + b*2 + 0), which simplifies to (4a + 2b = 4).Step: 5 ：Step 5: Solving the system of equations (begin{cases} a + b = 1 4a + 2b = 4end{cases}) we find that (a = 1) and (b = 0).

Given three points on a parabola, $P (0, 0)$ , $Q (1, 1)$ , and $R (2, 4)$ , find the equation of the parabola.

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Popular Problems

Given three points on a parabola, P(0,0), Q(1,1), and R(2,4), find the equation of the parabola.

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Popular Problems

Given three points on a parabola, $P (0, 0)$ , $Q (1, 1)$ , and $R (2, 4)$ , find the equation of the parabola.