Question

how do I write the equation of the parabola in intercept form​

Answer 1

Answer:

The equation of the parabola in intercept form is $y = -\frac{3}{4}\cdot x\cdot (x-4)$.

Step-by-step explanation:

The equation of the parabola in intercept form is defined by following formula:

$y = a\cdot (x-r_{1})\cdot (x-r_{2})$ (1)

Where:

$x$ - Independent variable.

$y$ - Dependent variable.

$a$ - Vertex constant.

$r_{1}, r_{2}$ - Intercepts of the parabola.

According to the graph, we find that intercepts are 0 and 4, respectively, and a point in the parabola is $(x,y) = (3, 2.25)$. If we know that $r_{1} = 0$, $r_{2} = 4$ and $(x,y) = (3, 2.25)$, then the vertex constant is:

$a = \frac{y}{(x-r_{1})\cdot (x-r_{2})}$

$a = -\frac{3}{4}$

The equation of the parabola in intercept form is $y = -\frac{3}{4}\cdot x\cdot (x-4)$.