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 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)
y is equal to negative 2 open paren x minus 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 \( y = a(x - p)(x - q) \), where \( p \) and \( q \) are the x-intercepts, we can start by using the given x-intercepts at (2, 0) and (4, 0). Thus, we have:

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

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

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

This simplifies to:

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

Now, solving for \( a \):

\[ a = \frac{6}{3} = 2 \]

Now we substitute \( a \) back into our intercept form equation:

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

Thus, the quadratic equation that accurately represents the given information is:

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

So, the correct response is:

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