Question

Write an equation of the parabola in intercept form that passes through (−2, 0.05) with x-intercepts of −7 and −3 . (in square meters) and x is the width (in meters). write an equation of the parabola. an equation of the parabola is y=

Answer 1

To write the equation of a parabola in intercept form, we can use the formula y=a(x-p)(x-q), where (p,0) and (q,0) are the x-intercepts. Given that the x-intercepts are -7 and -3, and the parabola passes through (-2, 0.05), the equation of the parabola is y=0.01(x+7)(x+3).

Step-by-step explanation:

To write the equation of a parabola in intercept form, we can use the formula y=a(x-p)(x-q), where (p,0) and (q,0) are the x-intercepts.

Given that the x-intercepts are -7 and -3, the equation becomes y=a(x+7)(x+3).

To find the value of a, we can use the fact that the parabola passes through (-2, 0.05), which gives us the equation 0.05=a(-2+7)(-2+3). Solving for a, we get a=0.01.

Therefore, the equation of the parabola in intercept form is y=0.01(x+7)(x+3).

Answer 2

The equation of the parabola in intercept form that passes through (-2, 0.05) with x-intercepts of -7 and -3 is y = x² + 10x + 21.

Step-by-step explanation:

To write the equation of a parabola in intercept form, we first need to find the x-intercepts.

The x-intercepts given in the question are -7 and -3.

Next, we need to find the y-intercept. The y-intercept given in the question is (−2, 0.05).

To find the equation in intercept form, we can use the equation (x - x1)(x - x2) = 0, where x1 and x2 are the x-intercepts. Plugging in the x-intercepts, we get (x + 7)(x + 3) = 0.

Expanding this equation, we get x² + 10x + 21 = 0.

Therefore, the equation of the parabola in intercept form is y = x² + 10x + 21.