Question

A parabola representing a quadratic equation has x-intercepts at (1,0)
and (−3,0)
and a third point with coordinates at (−1,4)
. Which quadratic equation in intercept form accurately represents this information?(1 point)
Responses

y=−1(x−1)(x−3)
y is equal to negative 1 open paren x minus 1 close paren open paren x minus 3 close paren

y=1(x−1)(x+3)
y is equal to 1 open paren x minus 1 close paren open paren x plus 3 close paren

y=−1(x+1)(x+3)
y is equal to negative 1 open paren x plus 1 close paren open paren x plus 3 close paren

y=−1(x−1)(x+3)

Answer 1

sorry wrong answer

Answer 2

To find the correct quadratic equation in intercept form, we start with the information provided:

1. The x-intercepts are (1,0) and (−3,0).
2. 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)**.