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

Write An Equation Of The Parabola In Intercept Form 3 4 4 0 2 0 An Equation Of The Parabola Is Y class=

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Question:

Solution:

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

[tex]y\text{ = }a(x-p)(x-q)[/tex]

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:

[tex]y\text{ = }a(x-2)(x-4)[/tex]

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

[tex]4\text{ = }a(3-2)(3-4)[/tex]

this is equivalent to:

[tex]4\text{ = }a(1)(-1)\text{ = -a}[/tex]

thus

[tex]a\text{ = -4}[/tex]

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

[tex]y\text{ = -4}(x-2)(x-4)[/tex]

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

[tex]y\text{ = -4}(x-2)(x-4)[/tex]

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