
(a)
To find:
The equation of the axis of symmetry, y -intercept and the x -cordinate of the vertex.
(a)

Answer to Problem 5CYU
V=(2,1)
Explanation of Solution
Given:
The given equation is
f(x)=4x2−6x−3
Concept used:
The standard form of parabola equation
y=ax2+bx+c
Putting x=h , y=k in equation (1)
k=ah2+bh+c.......................(2)
Where (h,k) is the vertex .
Calculation:
The standard form of parabola equation
y=ax2+bx+c
Putting x=h , y=k in equation (1)
k=ah2+bh+c(y−k)2=4a(x−h).......................(2)f(x)=4x2−6x−3
Where (h,k) is the vertex .
The vertex is
V=(2,1)
(b)
To show:
The table of the parabola is of the given form .
(b)

Explanation of Solution
Given:
The equation of parabola
f(x)=4x2−6x−3
Concept used:
The stabdard form of parabola equation
y=ax2+bx+c
Putting x=h , y=k in equation (1)
k=ah2+bh+c.......................(2)
Where (h,k) is the vertex .
Calculation:
The standard form of parabola equation
y=ax2+bx+c
Putting x=h , y=k in equation (1)
k=ah2+bh+c(y−k)2=4a(x−h).......................(2)
Where (h,k) is the vertex .
Draw the table
f(x)=4x2−6x−3
Test one point in each of the region formed by the graph .
If the point satisfies the function then shade the entire region to denote that every point in the region satisfies the function .
x−axis | −0.39 | 0 | 2 | −3.3 |
y−axis | 0 | −3 | 1 | 3 |
(c)
To show:
The graph of the parabola is of the given form .
(c)

Explanation of Solution
Given:
The equation of parabola
f(x)=4x2−6x−3
Concept used:
The stabdard form of parabola equation
y=ax2+bx+c
Putting x=h , y=k in equation (1)
k=ah2+bh+c.......................(2)
Where (h,k) is the vertex .
Calculation:
The stabdard form of parabola equation
y=ax2+bx+c
Putting x=h , y=k in equation (1)
k=ah2+bh+c(y−k)2=4a(x−h).......................(2)
Where (h,k) is the vertex .
Draw the graph
f(x)=4x2−6x−3
Test one point in each of the region formed by the graph .
If the point satisfies the function then shade the entire region to denote that every point in the region satisfies the function .
Chapter 5 Solutions
Algebra 2
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