What is the axis of symmetry and vertex for the graph #y= -7x^2 +2x#?

Question

Kennedy Adams · Accepted Answer

#x=1/7," vertex "=(1/7,1/7)# #"calculate the zeros by letting y = 0"# #-7x^2+2x=0# #x(-7x+2)=0# #x=0,x=2/7larrcolor(blue)"are the zeros"# #"the vertex lies on the axis of symmetry which is"# #"situated at the midpoint of the zeros"# #"axis of symmetry "x=(0+2/7)/2=1/7# #"substitute this value into the equation for y-coordinate"# #y=-7(1/7)^2+2(1/7)=-1/7+2/7=1/7# #color(magenta)"vertex "=(1/7,1/7)# graph{-7x^2+2x [-10, 10, -5, 5]}

Julia Adams · Answer

undefined The axis of symmetry for the graph $y = -7x^2 + 2x$ is the vertical line passing through the vertex. The formula to find the axis of symmetry is $x = -\frac{b}{2a}$, where $a$ is the coefficient of the $x^2$ term and $b$ is the coefficient of the $x$ term.

For $y = -7x^2 + 2x$, $a = -7$ and $b = 2$. 
So, the axis of symmetry is $x = -\frac{2}{2 \times -7} = \frac{1}{7}$.

To find the vertex, substitute the value of $x$ back into the equation to find the corresponding $y$ value.

When $x = \frac{1}{7}$, $y = -7(\frac{1}{7})^2 + 2(\frac{1}{7}) = -7(\frac{1}{49}) + \frac{2}{7} = -\frac{7}{49} + \frac{2}{7} = -\frac{5}{49}$.

So, the vertex is $(\frac{1}{7}, -\frac{5}{49})$.