Question

for the quadratic function f(x)= -x² - 2x, answer parts (a) through (f). (a) find the vertex and the axis of symmetry of the quadratic function, and determine whether the graph is concave up or concave down. the vertex is (-1,1). (type an ordered pair, using integers or fractions.) what is the equation of the axis of symmetry? the axis of symmetry is . (use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Recall axis - of - symmetry formula

For a quadratic function $y = ax^{2}+bx + c$, the axis of symmetry is given by $x=-\frac{b}{2a}$. For the function $f(x)=-x^{2}-2x$, where $a=-1$ and $b = - 2$.

Step2: Calculate the axis of symmetry

Substitute $a=-1$ and $b=-2$ into the formula $x =-\frac{b}{2a}$. We have $x=-\frac{-2}{2\times(-1)}=-\frac{-2}{-2}=-1$.

Answer:

$x = - 1$