**Finding the Equation of a Parabola Using a System of Equations****Problem:**Use a system of equations to find the equation of the parabola that contains the three given points: (0,7), (1,4), and (3,-8). Write your answer in the form of: \( y = ax^2 + bx + c \).**Instructions:**1. Identify the general form of a parabolic equation: \( y = ax^2 + bx + c \).2. Substitute each of the given points into the equation to create a system of equations. - For the point (0,7): \[ 7 = a(0)^2 + b(0) + c \] \[ 7 = c \] - For the point (1,4): \[ 4 = a(1)^2 + b(1) + c \] \[ 4 = a + b + c \] - For the point (3,-8): \[ -8 = a(3)^2 + b(3) + c \] \[ -8 = 9a + 3b + c \]3. Plug in the value of \( c \) found from the first equation into the other equations.**Solution:**Follow the steps outlined to solve the system of equations and find values for \( a \), \( b \), and \( c \). **Additional Notes:**- Ensure to check your final equation by substituting the original points (0,7), (1,4), and (3,-8) back into the equation to verify its accuracy.**Student Task:**Student can enter maximum 2000 characters in the provided text box.Additionally, a paperclip button is available below to attach files, if needed.

Three points are (0,7) , (1,4) and ,(3, -8)

Use a system of equations to find the equation of the parabola that contains the three given points: (0,7),(1,4), and (3,-8) Write your answer in the form of: y = ax + bx+c. *Student can enter max 2000 characters XDGB I U Use the paperclip button below to attach files.

Use a system of equations to find the equation of the parabola that contains the three given points: (0,7),(1,4), and (3,-8) Write your answer in the form of: y = ax + bx+c. *Student can enter max 2000 characters XDGB I U Use the paperclip button below to attach files.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter7: Conic Sections And Quadratic Systems

Section7.4: Solving Nonlinear Systems Of Equations

Problem 64E: Determine if the statement is true or false. If the statement is false, then correct it and make it...

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Question

**Finding the Equation of a Parabola Using a System of Equations**

**Problem:**
Use a system of equations to find the equation of the parabola that contains the three given points: (0,7), (1,4), and (3,-8). Write your answer in the form of: \( y = ax^2 + bx + c \).

**Instructions:**
1. Identify the general form of a parabolic equation: \( y = ax^2 + bx + c \).
2. Substitute each of the given points into the equation to create a system of equations.

- For the point (0,7):
\[ 7 = a(0)^2 + b(0) + c \]
\[ 7 = c \]

- For the point (1,4):
\[ 4 = a(1)^2 + b(1) + c \]
\[ 4 = a + b + c \]

- For the point (3,-8):
\[ -8 = a(3)^2 + b(3) + c \]
\[ -8 = 9a + 3b + c \]

3. Plug in the value of \( c \) found from the first equation into the other equations.

**Solution:**
Follow the steps outlined to solve the system of equations and find values for \( a \), \( b \), and \( c \).

**Additional Notes:**
- Ensure to check your final equation by substituting the original points (0,7), (1,4), and (3,-8) back into the equation to verify its accuracy.

**Student Task:**
Student can enter maximum 2000 characters in the provided text box.
Additionally, a paperclip button is available below to attach files, if needed.

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Step 1: To find the parabolic equation in standard form, which contains 3 points .

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