Question

Use quadratic regression to find the

equation for the parabola going
through these 3 points.
(-4, 7) (6, -33) (10, -105)
y = -1x² + [ ? ]x + [ ? ]

Answer 1

To find the equation for the parabola going through the given points using quadratic regression, we can use the quadratic formula. The equation for the parabola is y = -1x² + 7x - 8.

Step-by-step explanation:

To find the equation for the parabola going through the points (-4, 7), (6, -33), and (10, -105) using quadratic regression, we need to use the quadratic formula. Let's first calculate the values of a, b, and c in the quadratic equation ax² + bx + c = 0:

• For point (-4, 7): 7 = a*(-4)² + b*(-4) + c
• For point (6, -33): -33 = a*(6)² + b*(6) + c
• For point (10, -105): -105 = a*(10)² + b*(10) + c

Solving these equations, we get a = -1, b = 7, and c = -8. The equation for the parabola is y = -1x² + 7x - 8.

Answer 2

To find the equation of the parabola that passes through the given points using quadratic regression, substitute the x and y coordinates of each point into the equation y = ax^2 + bx + c and solve for the constants a, b, and c. The equation for the parabola is y = -1x^2 + 3.59x - 9.22.

Step-by-step explanation:

To find the equation of the parabola that passes through the given points, we can use quadratic regression. Quadratic regression provides an equation of the form y = ax^2 + bx + c, where a, b, and c are constants. We can substitute the x and y coordinates of each point into the equation to find the values of a, b, and c. Substituting (-4, 7), (6, -33), and (10, -105) into the equation, we can solve for a, b, and c.

This gives us the equation: y = -1x^2 + 3.59x - 9.22.