Write an equation of the parabola in intercept form. (3, 4) (4, 0) (2, 0) An equation of the parabola is y=

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asked May 15, 2023 34.0k views

1 Answer

Shan Plourde · Answer 1 · 2023-05-22T13:24:29+0000

Question:

Solution:

The intercept form of a quadratic equation (a parabola) is given by the following formula:

$y\text{ = }a(x-p)(x-q)$

where p and q are the x-coordinate of the x-intercept of the parabola. In this case, notice that:

p = 2 and q = 4

then we have the preliminary equation:

EQUATION 1:

$y\text{ = }a(x-2)(x-4)$

now, to find a, replace the point (x,y) = (3,4) in the previous equation. so that, we obtain:

$4\text{ = }a(3-2)(3-4)$

this is equivalent to:

$4\text{ = }a(1)(-1)\text{ = -a}$

thus

$a\text{ = -4}$

then, replacing a = -4 into the EQUATION 1, we get:

$y\text{ = -4}(x-2)(x-4)$

Then, we can conclude that the equation of the given parabola in the intercept form is:

$y\text{ = -4}(x-2)(x-4)$