A parabola representing a quadratic equation has x-intercepts at (2,0)

Question

(
2
,
0
)
and (4,0)
(
4
,
0
)
and a third point with coordinates at (5,6)
(
5
,
6
)
. Which quadratic equation in intercept form accurately represents this information?(1 point)
Responses

y=2(x+2)(x−4)
𝑦
=
2
(
𝑥
+
2
)
(
𝑥
−
4
)
y is equal to 2 open paren x plus 2 close paren open paren x minus 4 close paren

y=2(x−2)(x−4)
𝑦
=
2
(
𝑥
−
2
)
(
𝑥
−
4
)
y is equal to 2 open paren x minus 2 close paren open paren x minus 4 close paren

y=2(x−2)(x+4)
𝑦
=
2
(
𝑥
−
2
)
(
𝑥
+
4
)
y is equal to 2 open paren x minus 2 close paren open paren x plus 4 close paren

y=−2(x−2)(x−4)

Answer 1

To find the correct quadratic equation in intercept form given the x-intercepts and another point, we start with the intercept form of a quadratic equation:

\[ y = a(x - p)(x - q) \]

where \( p \) and \( q \) are the x-intercepts.

In this case, the x-intercepts are \( (2, 0) \) and \( (4, 0) \). Therefore, our equation starts as:

\[ y = a(x - 2)(x - 4) \]

Next, we need to find the value of \( a \) using the third point \( (5, 6) \).

Plugging this point into the equation:

• \( x = 5 \)
• \( y = 6 \)

Substituting these values:

\[ 6 = a(5 - 2)(5 - 4) \] \[ 6 = a(3)(1) \] \[ 6 = 3a \] \[ a = \frac{6}{3} = 2 \]

Now, substituting \( a \) back into the equation gives us:

\[ y = 2(x - 2)(x - 4) \]

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

y = 2(x - 2)(x - 4)