# How do you find the y intercept, the equation of

How do you find the y intercept, the equation of the axis of symmetry and the x-coodinate of the vertex
$f\left(x\right)={x}^{2}-10x+5?$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

enguinhispi
Step 1
y-intercept is 5, Axis of symmetry is $x=5$, x-coordinate of vertex is 5.
To find the axis of symmetry, and the coordinates of the vertex, this quadratic function need be put in its standard form (parabola):
$y={x}^{2}-10x+5$
$={x}^{2}-10x+25-25+5$
$={\left(x-5\right)}^{2}-20$
$y+20={\left(x-5\right)}^{2}$
Compare this with the standard form of a vertical parabola $y-k={\left(x-h\right)}^{2}$ with vertex and axis of symmetry $x=h$
The vertex is therefore and axis of symmetry is $x=5$