Answer:
Draw a line at y = -5.
x ≈ -3.5
x ≈ 1
Step-by-step explanation:
Given equation:
[tex]y = -2x^2 - 5x + 2[/tex]
This is the equation of the graphed parabola.
To solve the equation [tex]-2x^2 - 5x + 2 = -5[/tex] draw a line at y = -5 and find the points of intersection of the two graphed equations.
From inspection of the graph, the x-values of the points of intersection are:
Solving algebraically
Add 5 to both sides of the equation:
[tex]\implies -2x^2-5x+2+5=-5+5[/tex]
[tex]\implies -2x^2-5x+7=0[/tex]
Factor out -1 from the left side:
[tex]\implies -1(2x^2+5x-7)=0[/tex]
Divide both sides by -1:
[tex]\implies 2x^2+5x-7=0[/tex]
Find two numbers that multiply to -14 and sum to 5: 7 and -2
Rewrite b as the sum of these two numbers:
[tex]\implies 2x^2+7x-2x-7=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(2x+7)-1(2x+7)=0[/tex]
Factor out the common term (2x + 7):
[tex]\implies (x-1)(2x+7)=0[/tex]
Apply the zero-product property:
[tex](x-1)=0 \implies x=1[/tex]
[tex](2x+7)=0 \implies x=-\dfrac{7}{2}=-3.5[/tex]
