A quadratic relation has zeros at 3 and –5. The parabola goes through the point (2, –14). What is the equation of the parabola in standard form?

Step-by-step explanation:

we are given the zeros and a point where it goes through of a quadratic equation

remember that when the roots are given then the function should be

where a is the leading coefficient and x1 and x2 are the roots

substitute:

simplify:

now the given point tells us that when x is 2 y is -14 therefore by using the point we can figure out a

substitute:

simplify parentheses:

simplify multiplication:

divide both sides by -7:

altogether substitute:

since it want the equation y should be

recall quadratic equation standard form:

so simplify parentheses:

distribute:

hence,

the equation of the parabola in standard form is 2x²+4x-30=0

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,