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Korolek [52]
4 years ago
10

Rewrite the following quadratic function in vertex form. Then, determine the axis of symmetry. y=5x^2+15x-2

Mathematics
2 answers:
omeli [17]4 years ago
5 0
5x^2+15x-2
5(x^2+3x)-2
5(x^2+3x+2.25-2.25)-2
5(x^2+3x+2.25)-13.25
5(x+1.5)^2-13.25

final answer: y=5(x+1.5)^2-13.25
axis of symmetry: (1.5, 13.25)
Daniel [21]4 years ago
4 0

Answer:  The vertex form of the given function is y=5\left(x+\dfrac{3}{2}\right)^2-\dfrac{53}{4} and its axis of symmetry is x=-\dfrac{3}{2}.

Step-by-step explanation:  The given quadratic function is

y=5x^2+15x-2~~~~~~~~~~~~~~(i)

We are to rewrite the above function in vertex form and to determine its axis of symmetry.

We have from equation (i),

y=5x^2+15x-2\\\\\Rightarrow y=5(x^2+3x)-2\\\\\Rightarrow y=5\left(x^2+2\times x\times \dfrac{3}{2}+\dfrac{9}{4}\right)-\dfrac{45}{4}-2\\\\\Rightarrow y=5\left(x+\dfrac{3}{2}\right)^2-\dfrac{45+8}{4}\\\\\Rightarrow y=5\left(x+\dfrac{3}{2}\right)^2-\dfrac{53}{4}.

So, the given function is a parabola with vertex at the point \left(-\dfrac{3}{2},-\dfrac{53}{4}\right).

Therefore, the axis of symmetry is given by

x=-\dfrac{3}{2}.

Thus, the vertex form of the given function is y=5\left(x+\dfrac{3}{2}\right)^2-\dfrac{53}{4} and its axis of symmetry is x=-\dfrac{3}{2}.

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