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What are the coordinates of the vertex of the parabola?

y=3/4x^2−6x+15

User Felix Cen
by
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1 Answer

2 votes

Answer:

The vertex is the point (4,3)

Explanation:

we have


y=(3)/(4)x^(2)-6x+15

Convert to vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation


y-15=(3)/(4)x^(2)-6x

Factor the leading coefficient


y-15=(3)/(4)(x^(2)-8x)

Complete the square. Remember to balance the equation by adding the same constants to each side.


y-15+12=(3)/(4)(x^(2)-8x+16)


y-3=(3)/(4)(x^(2)-8x+16)

Rewrite as perfect squares


y-3=(3)/(4)(x-4)^(2)


y=(3)/(4)(x-4)^(2)+3 ----> equation in vertex form

The vertex is the point (4,3)

User Fazeel Qureshi
by
6.8k points