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sukhopar [10]
3 years ago
10

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of y=4x^2+5x-1

Mathematics
1 answer:
Ivanshal [37]3 years ago
4 0
Answer:

Axis of symmetry: x=-\frac{5}{8}

Vertex: (-\frac{5}{8},-2\frac{9}{16})

Step-by-step explanation:

The given quadratic equation is

y=4x^2+5x-1

By comparing to the general quadratic function; y=ax^2+bx+c

We have a=4,b=5,c=-1

The equation of the axis of symmetry is given by the formula;

x=-\frac{b}{2a}

We got this formula by completing the square on the general quadratic function.

We substitute a=4 and b=5 to obtain;

x=-\frac{5}{2(4)}

x=-\frac{5}{8}
is the axis of symmetry.

To find the y-value of the vertex, we put x=-\frac{5}{8} into the function to obtain;

y=4(-\frac{5}{8})^2+5(-\frac{5}{8})-1

y=4(-\frac{5}{8})^2+5(-\frac{5}{8})-1

y=-\frac{41}{16}

The vertex of the given function is (-\frac{5}{8},-2\frac{9}{16})
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