To find the correct quadratic equation in intercept form that represents the given information, we can start from the x-intercepts.
We know that the x-intercepts are at \( (1, 0) \) and \( (-3, 0) \). The quadratic equation in intercept form can be expressed as:
\[ y = a(x - r_1)(x - r_2) \]
where \( r_1 \) and \( r_2 \) are the x-intercepts and \( a \) is a constant that determines the orientation and steepness of the parabola. In this case, since the intercepts are \( r_1 = 1 \) and \( r_2 = -3 \), this gives us:
\[ y = a(x - 1)(x + 3) \]
Now, to determine the value of \( a \), we can use the third point given, which is \((-1, 4)\). Plugging the coordinates of this point into the equation gives us:
\[ 4 = a(-1 - 1)(-1 + 3) \]
Calculating the terms inside the parentheses:
\[ 4 = a(-2)(2) \] \[ 4 = -4a \]
Solving for \( a \):
\[ a = -1 \]
Now we substitute \( a \) back into the equation:
\[ y = -1(x - 1)(x + 3) \]
Thus, the quadratic equation that accurately represents this information is:
\[ y = -1(x - 1)(x + 3) \]
So, the correct response is:
y = −1(x−1)(x+3).