Question

Write the equation for the parabola that has x− intercepts (1.2,0) and (4,0) and y− intercept (0,12).

Answer 1

Equation of a parabola is written in the form of f(x)=ax²+bx+c.
The equation passes through points (4,0), (1.2,0) and (0,12), therefore; 
 replacing the points in the equation y = ax² +bx+c 
we get  0 = a(4)²+b(4) +c   for (4,0)
             0 = a (1.2)²+ b(1.2) +c for (1.2,0)
             12 = a(0)² +b(0) +c   for (0,12)
simplifying the equations we get
16a + 4b + c = 0
1.44a +1.2b + c = 0
+c = 12
thus the first two equations will be
16a + 4b = -12
1.44 a + 1.2b = -12 solving simultaneously 
the value of a = 5/2 and b =-13
Thus, the equation of the parabola will be given by;
 y= 5/2x² - 13x + 12 or y = 2.5x² - 13x + 12

Answer 2

The equation for the parabola that has x-intercepts (1.2,0) and (4,0) and y-intercept (0,12) is $\rm y=\dfrac{5}{2}x^2 - 13x + 12$.

What is the standard form of a parabola?

The standard form of a parabola can be represented as;

$\rm y=ax^2+bx+c$

The equation passes through points (4,0), (1.2,0), and (0,12), therefore replacing the points in the equation.

The equation we get from point (4, 0) is;

$\rm 0 = a(4)^2+b(4) +c\\\\16a+4b+c=0$

The equation we get from point (1.2, 0) is;

$\rm 0 = a (1.2)^2+ b(1.2) +c\\\\1.44a +1.2b + c = 0$

The equation we get from point (0, 12) is;

$\rm 12 = a(0)^2 +b(0) +c\\\\c=12$

Substitute the value of c in equation 1

$\rm 16a + 4b + c = 0\\\\16a+4b +12=0\\\\16a+4b=-12\\\\4a+b=-3\\\\ b = -3-4a$

Substitute the value of b and c in equation 2

$\rm 1.44a +1.2b + c = 0\\\\1.44a+1.2(-3-4a)+12=0\\\\1.44a -3.6-4.8a+12=0\\\\-3.36a+8.4=0\\\\-3.36a=-8.4\\\\a=\dfrac{-8.4}{-3.36}\\\\a=\dfrac{5}{2}$

Substitute all the values in the equation of a parabola

$\rm y=ax^2+bx+c\\\\ y=\dfrac{5}{2}x^2 - 13x + 12$

Hence, the equation for the parabola that has x-intercepts (1.2,0) and (4,0) and y-intercept (0,12) is $\rm y=\dfrac{5}{2}x^2 - 13x + 12$.

To know more about parabola click the link given below.

https://brainly.com/question/12058812

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