Taxes -1 and 2 y is 10 and 2,160 the equation is y equals blank times blank squared

1 answer

It seems like you're trying to find a quadratic equation given some specific values. It looks like you have two points that might define this equation, possibly indicating an input-output relationship (like a tax calculation).

From your message, it seems like you have two pairs of values for \( y \):

  1. When \( x = -1 \), \( y = 10 \)
  2. When \( x = 2 \), \( y = 2160 \)

You are looking for a quadratic equation in the form of \( y = ax^2 + bx + c \). To find the coefficients \( a \), \( b \), and \( c \), we can set up a system of equations based on these points.

  1. For \( x = -1 \): \[ 10 = a(-1)^2 + b(-1) + c \implies 10 = a - b + c \quad \text{(Equation 1)} \]

  2. For \( x = 2 \): \[ 2160 = a(2)^2 + b(2) + c \implies 2160 = 4a + 2b + c \quad \text{(Equation 2)} \]

To fully determine the equation, we usually need a third point. However, we can also make an assumption about the form of the quadratic equation to simplify it. Let’s assume \( y = ax^2 \), which would fit the general quadratic form, ignoring the linear \( bx + c \) component initially for simplicity.

From the point \( (2, 2160) \): \[ 2160 = a(2^2) \implies 2160 = 4a \implies a = 540 \]

The equation \( y = 540x^2 \) fits the first point to some degree since there is no linear term to influence it. To check it, we can substitute:

For \( x = -1 \): \[ y = 540(-1)^2 = 540 \] This does not match \( y = 10 \), indicating we need the linear terms.

Since you mentioned different formats in your prompt (“blank times blank squared”), we realize that we likely need a complete expression.

General Path Forward

  1. Form three simultaneous equations from the points, aiming for \( y = ax^2 + bx + c \).
  2. Check values and determine if you need to constrain your model further for reasoning (like whether \( c = 0 \) or fixing \( b \)).

The standard way to manage a quadratic here is:

  1. Calculate it exactly.
  2. Graph it and find coefficients or explore if further assumptions apply (via constraints).

If you want to follow up with another point or if you have more requirements (like \( c \) being zero), please clarify!