Question

Find the coordinates of the vertex and write the equation of the axis of symmetry. $$y=-4 x^{2}-2 x+5$$

Short answer

The vertex of the function is (-1/4, 4.5) and the axis of symmetry is \(x = -1/4\).

Step-by-step solution

Identify coefficients a and b

For this quadratic equation, \(y = -4x^{2} - 2x + 5\), the coefficient 'a' is -4 and the coefficient 'b' is -2.

Find the x-coordinate of Vertex

The formula to find the x-coordinate of the vertex is \(-b/2a\). Substituting the values of 'a' and 'b', we get x coordinate as \((-(-2))/2(-4) = -1/4\).

Find the y-coordinate of Vertex

To find the y-coordinate of the vertex, replace 'x' in the original equation with the x-coordinate of the vertex found in the previous step. So, \(y = -4(-1/4)^{2} - 2(-1/4) + 5 = 5 -0.5 = 4.5 \)

Find the equation of Axis of Symmetry

The equation of the axis of symmetry for a parabola is \(x = -b/2a\). We already found this value in Step 2, so the axis of symmetry is \(x = -1/4\)