Once you use a formula to find the vertex of a parabola how

Once you use a formula to find the vertex of a parabola, how can you determine if it is a maximum of minimum value? When simplifying rational expressions with complex numbers in the denominator, why do we multiply the top and bottom of the given fraction by the conjugate of the denominator? How do you find the x-intercepts and y-intercepts of graph of an equation? What is the equation of the x-axis? What is the equation of the y-axis? Why ? Why does the \"vertical line test\" help us to identify functions versus non-functions? What is a rational function?, how can you determine the vertical and horizontal asymptotes of rational functions?

Solution

9)y coordinate of the vertex gives the maximum or minimum value .

when parabola opens upwards ,the y coordinate gives minimum value

when parabola opens downwards ,the y coordinate gives maximum value

for y=ax^2 +bx +c, when a>0 ,parabola opens upwards , when a<0 ,parabola opens downwards

10)we multiply the top and bottom of the given fraction by conjegate of the denominator to rationalise the denominator so that there will not be any more complex number in denominator which results in the simplest from .

11. for x intercept we put y=0 and solve for values of x

for y intercept we put x=0 and solve for values of y

12)equation of x axis is y =0 because for all the points on x axis their y coordinate is zero

equation of y axis is x =0 because for all the points on y axis their x coordinate is zero

13)at a given particular x value ,a given function should have single corresponding y value.that can be tested by vertical line, when vertical line intersects the curve more that once then the curve doesnot represent a function

14)rational function is a fraction of 2 polynomials,

we get vertical asymptote by equating denominator to zero

we get horizontal asymptote taking the limit of function at infinity and - infinity