Question

Write the formula for the parabola that has x- intercepts (−3−sqrt(2) ,0) and (−3+sqrt(2) ,0), and y- intercept (0,−5)

Answer 1

Answer:

$y=-\frac{5}{7}x^2-\frac{30}{7}x-5$

Step-by-step explanation:

we know that

The equation of a vertical parabola in factored form is given by

$y=a(x-x_1)(x-x_2)$

where

a is the leading coefficient

x_1 and x_2 are the x-intercepts

substitute

$y=a(x-(-3-\sqrt{2}))(x-(-3+\sqrt{2}))$

$y=a(x+(3+\sqrt{2}))(x+(3-\sqrt{2}))$

Convert to expanded form

$y=a(x^2+x(3-\sqrt{2})+x(3+\sqrt{2})+7)$

$y=a(x^2+6x+7)$

Find the value of a

we have the y-intercept (0,-5)

substitute in the equation the value of x and the value of y

$-5=a(0^2+6(0)+7)$

$-5=7a\\a=-\frac{5}{7}$

therefore

$y=-\frac{5}{7}(x^2+6x+7)$

$y=-\frac{5}{7}x^2-\frac{30}{7}x-5$