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The vertex of this parabola is at (3,-2). When the x-value is 4, the y-value is 3. What is the coefficient of the squared expression in the parabolas equation?

a. -1
b. 5
c. 1
d. 7

( Please show your work, I would like to know how its done. Thankyou <3 )

User Mcwong
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1 Answer

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The vertex of this parabola is at (3,-2). When the x-value is 4, the y-value is 3: (4,3) is a point on the parabola. Let's use the standard equation of a parabola in vertex form:

y-k = a(x-h)^2, where (h,k) is the vertex (here (3,-2)) and (x,y): (4,3) is another point on the parabola. Since (3,-2) is the lowest point of the parabola, and (4,3) is thus higher up, we know that the parabola opens up.

Substituting the given info into the equation y-k = a(x-h)^2, we get:

3-[-2] = a(4-3)^2, or 5 = a(1)^2. Thus, a = 5, and the equation of the parabola is

y+2 = 5(x-3)^2 The coefficient of the x^2 term is thus 5.

User Spatialist
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