Answer:
The other point of intersection is (1.5,4.5)
Step-by-step explanation:
The correct quadratic equation is
[tex]y=-2x^2+4x+3[/tex]
step 1
Find he y-intercept of the parabola
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
[tex]y=-2(0)^2+4(0)+3=3[/tex]
therefore
The y-intercept is the point (0,3)
step 2
Find the equation of the line
The equation in slope intercept form is
[tex]y=mx+b[/tex]
we have
[tex]m=1\\b=3[/tex]
substitute
[tex]y=x+3[/tex]
step 3
Find the other point of intersection
we have
[tex]y=-2x^2+4x+3[/tex]
[tex]y=x+3[/tex]
Equate both equations
[tex]-2x^2+4x+3=x+3[/tex]
solve for x
[tex]-2x^2+3x=0[/tex]
[tex]2x^2=3x[/tex]
we know that one solution is x=0
simplify x
[tex]2x=3\\x=1.5[/tex]
Find the value of y
substitute the value of x in any equation (line or parabola)
[tex]y=1.5+3=4.5[/tex]
therefore
The other point of intersection is (1.5,4.5)
