MHB Making up an Equation That Satisfies Given Conditions

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An equation that satisfies the conditions of having x-intercepts at (-1, 0) and (2, 0) and a y-intercept at (0, 4) can be expressed as y = k(x - 2)(x + 1). To determine the value of k, substitute y = 4 and x = 0 into the equation. This allows for solving k to ensure the equation meets the specified intercepts. The discussion emphasizes the importance of correctly factoring in the y-intercept when forming the equation. Ultimately, the approach leads to a valid quadratic equation that meets all given conditions.
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Make up an equation that satisfies the given conditions: must have x-intercepts at (-1, 0) and (2, 0). It must also have a y-intercept at (0, 4).

Is it correct to say that the equation with x-intercepts would look like this:

y = (x - 2) (x + 1)How do you factor the y-intercept?
 
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Re: Making up an Equation Satisfies Given Conditions

Joystar1977 said:
Make up an equation that satisfies the given conditions: must have x-intercepts at (-1, 0) and (2, 0). It must also have a y-intercept at (0, 4).

Is it correct to say that the equation with x-intercepts would look like this:

y = (x - 2) (x + 1)How do you factor the y-intercept?

You are definitely on the right track. I would use the form:

$$y=k(x-2)(x+1)$$

Now let $y=4$ and $x=0$ and solve for $k$. :D
 
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