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

Question

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

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)
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 is equal to 2 open paren x plus 2 close paren open paren x minus 4 close paren

y=−2(x−2)(x−4)

Answer 1

To find the quadratic equation in intercept form that meets the given conditions, we can start by using the x-intercepts. The intercept form of a quadratic equation with given x-intercepts \( x_1 \) and \( x_2 \) is:

\[ y = a(x - x_1)(x - x_2) \]

Given the x-intercepts at \( (2,0) \) and \( (4,0) \), we can write:

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

Next, we need to determine the value of \( a \) using the third point \( (5, 6) \). We substitute \( (x, y) = (5, 6) \) into the equation:

\[ 6 = a(5 - 2)(5 - 4) \]

This simplifies to:

\[ 6 = a(3)(1) \] \[ 6 = 3a \] \[ a = 2 \]

Now substitute \( a = 2 \) back into the equation:

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

This is the quadratic equation in intercept form that accurately represents the information given.

Therefore, the correct response is:

y = 2(x−2)(x−4)