To find the correct quadratic equation in intercept form, we start with the information provided:
- The x-intercepts are (1,0) and (−3,0).
- There is a point on the parabola at (−1, 4).
The intercept form of a quadratic equation is given by:
\[ y = a(x - p)(x - q) \]
where \( p \) and \( q \) are the x-intercepts.
In this case, our intercepts are \( p = 1 \) and \( q = -3 \). Therefore, the equation can be initially written as:
\[ y = a(x - 1)(x + 3) \]
Next, we can use the third point (−1, 4) to find the value of \( a \). Plugging \( x = -1 \) and \( y = 4 \) into the equation:
\[ 4 = a(-1 - 1)(-1 + 3) \]
Calculating the factors:
- \( -1 - 1 = -2 \)
- \( -1 + 3 = 2 \)
Now we can substitute these values into the equation:
\[ 4 = a(-2)(2) \] \[ 4 = -4a \]
Solving for \( a \):
\[ a = -1 \]
Now we can substitute \( a \) back into the equation:
\[ y = -1(x - 1)(x + 3) \]
Thus, the correct quadratic equation that represents the information given is:
\[ y = -1(x - 1)(x + 3) \]
So, the answer is:
y = −1(x−1)(x+3).