Question

write an equation of the parabola in intercept form. an equation of the parabola is y =

Explanation:

Step1: Recall intercept - form of parabola

The intercept - form of a parabola is $y = a(x - p)(x - q)$, where $p$ and $q$ are the $x$ - intercepts. From the graph, the $x$ - intercepts are $x = 2$ and $x = 4$, so $p = 2$ and $q = 4$. Then the equation is $y=a(x - 2)(x - 4)$.

Step2: Find the value of $a$

We know that the parabola passes through the point $(3,4)$. Substitute $x = 3$ and $y = 4$ into the equation $y=a(x - 2)(x - 4)$.
$4=a(3 - 2)(3 - 4)$
$4=a(1)(-1)$
$a=-4$

Answer:

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