Question

The graph of y=
-2x²5x+2 is drawn below
Draw a suitable line to solve -2x² - 5x + 2 = -5

Answer 1

x = 1 and x = -3.5

Explanation:

y = -2x² -5x + 2

-2x² -5x + 2 = -5

which means y = -5

Draw the line on y = -5 like the green line in the attached file

and see where this line intersects with the graph

the values are:

x = 1 and x = -3.5

Answer 2

Draw a line at y = -5.

x ≈ -3.5

x ≈ 1

Explanation:

Given equation:

`y = -2x^2 - 5x + 2`

This is the equation of the graphed parabola.

To solve the equation
`-2x^2 - 5x + 2 = -5` 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:

• x ≈ -3.5
• x ≈ 1

Solving algebraically

Add 5 to both sides of the equation:

`\implies -2x^2-5x+2+5=-5+5`

`\implies -2x^2-5x+7=0`

Factor out -1 from the left side:

`\implies -1(2x^2+5x-7)=0`

Divide both sides by -1:

`\implies 2x^2+5x-7=0`

Find two numbers that multiply to -14 and sum to 5: 7 and -2

Rewrite b as the sum of these two numbers:

`\implies 2x^2+7x-2x-7=0`

Factor the first two terms and the last two terms separately:

`\implies x(2x+7)-1(2x+7)=0`

Factor out the common term (2x + 7):

`\implies (x-1)(2x+7)=0`

Apply the zero-product property:

`(x-1)=0 \implies x=1`

`(2x+7)=0 \implies x=-(7)/(2)=-3.5`