To find the quadratic equation in intercept form that has x-intercepts at (1,0) and (3,0) and passes through the point (4,3), we start with the intercept form of the quadratic equation:
\[ y = a(x - p)(x - q) \]
where \( p \) and \( q \) are the x-intercepts of the parabola.
From the given information, we have:
- \( p = 1 \)
- \( q = 3 \)
Thus, the equation becomes:
\[ y = a(x - 1)(x - 3) \]
Next, we need to find the value of \( a \) using the additional point (4,3). Substituting \( x = 4 \) and \( y = 3 \) into the equation gives:
\[ 3 = a(4 - 1)(4 - 3) \] \[ 3 = a(3)(1) \] \[ 3 = 3a \] \[ a = 1 \]
Now we can write the complete quadratic equation:
\[ y = 1(x - 1)(x - 3) \] or simply,
\[ y = (x - 1)(x - 3) \]
Therefore, the correct answer is:
y = 1(x−1)(x−3)
This corresponds to the response:
y is equal to 1 open paren x minus 1 close paren open paren x minus 3 close paren.
2 answers