210k views
2 votes
Function = y=(x-4)^2-5+7

Calculate the x and y values for the vertex point of the parabola.
State what the axis of symmetry is.
Set your quadratic function to zero (let y = 0) and use either the quadratic formula or completing the square method to solve for the two solutions of x when y = 0
Calculate the discriminant for the quadratic equation.

User Norym
by
7.9k points

1 Answer

5 votes

Given equation of parabola is
y=(x-4)^2-5+7

Or we can simplify that to
y=(x-4)^2+2

This equaion looks similar to formula
y=a(x-h)^2+k

Comparing both equation, we get:

a=1, h=4, k=2

(h,k) represents the vertex of the parabola

Hence vertex of the given parabola is (4,2).


So x-value of the vertex = 4

So y-value of the vertex = 2


Axis of symmetry is given by equation x=h

So the answer will be x=4


Now we will set y=0 and solve this using quadratic formula including desriminant


0=(x-4)^2+2


0=x^2-8x+16+2


0=x^2-8x+18

compare with quadratic equation
0=ax^2+bx+c, we get:

a=1, b=-8, c=18

Descriminant is given by formula:


Descriminant = √(b^2-4ac) = √((-8)^2-4(1)(18))= √(-8)= -2√(2) i

which is imaginary

Hence there will be no real solution for x-intercept.

User Avnic
by
8.3k points

No related questions found