A parabola representing a quadratic equation has x-intercepts at (1,0)

Question

(
1
,
0
)
and (3,0)
(
3
,
0
)
and a third point with coordinates at (4,3)
(
4
,
3
)
. Which quadratic equation in intercept form accurately represents this information?(1 point)
Responses

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

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

y=−1(x−1)(x−3)

Answer 1

The x-intercepts of the parabola are given as (1, 0) and (3, 0). Therefore, we can express the quadratic equation in intercept form as:

\[ y = a(x - 1)(x - 3) \]

where \( a \) is a coefficient that we need to determine.

Next, we have a third point (4, 3) that lies on the parabola. We can substitute \( x = 4 \) and \( y = 3 \) into the equation to find the value of \( a \):

\[ 3 = a(4 - 1)(4 - 3) \] \[ 3 = a(3)(1) \] \[ 3 = 3a \] \[ a = 1 \]

Now we can write the full equation of the parabola:

\[ y = 1(x - 1)(x - 3) \]

Thus, the quadratic equation in intercept form that accurately represents the information is:

y = 1(x - 1)(x - 3)

This option matches the first response choice in the original question.