for the quadratic function f(x)= -x² - 2x, answer parts (a) through (f). (a) find the vertex and the axis of…

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 . (type an ordered pair, using integers or fractions.)

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 . (type an ordered pair, using integers or fractions.)

Answer

Answer:

(-1, 1)

Explanation:

Step1: Identify coefficients

For $f(x)=-x^{2}-2x$, $a = - 1$, $b=-2$, $c = 0$.

Step2: Find x - coordinate of vertex

Use formula $x=-\frac{b}{2a}$. Substitute $a=-1$ and $b = - 2$: $x=-\frac{-2}{2\times(-1)}=-1$.

Step3: Find y - coordinate of vertex

Substitute $x = - 1$ into $f(x)$: $f(-1)=-(-1)^{2}-2\times(-1)=-1 + 2=1$.

Step4: Determine axis of symmetry

Axis of symmetry is $x=-1$ (same as x - coordinate of vertex).

Step5: Determine concavity

Since $a=-1<0$, the graph is concave down.