Is a Quadratic Equation with b=0 or c=0 Still a Quadratic?

Click For Summary
A quadratic equation is defined as having the form y = ax^2 + bx + c, where a is not equal to zero. Even if c = 0, resulting in y = ax^2 + bx, it remains a quadratic equation. Similarly, if b = 0, leading to y = ax^2, it is still classified as a quadratic equation due to the presence of the x^2 term. The key factor is that the coefficient a must not be zero for it to retain its quadratic classification. Thus, both cases of b = 0 and c = 0 still qualify as quadratic equations.
LearninDaMath
Messages
295
Reaction score
0
A quadratic equation has the form y = ax^2 + bx + c. However, if c = 0, then y = ax^2 + bx. Is it still called a quadratic equation? And if b = 0 so that y = ax^2, is it still given the title of quadratic equation?

I would guess yes since it still has a power of 2 and is a parabola. Is this correct?
 
Mathematics news on Phys.org
LearninDaMath said:
A quadratic equation has the form y = ax^2 + bx + c.
What you're showing is a quadratic function. A quadratic equation in standard form looks like this:
ax2 + bx + c = 0
LearninDaMath said:
However, if c = 0, then y = ax^2 + bx. Is it still called a quadratic equation?
ax2 + bx = 0 is still a quadratic equation. The only restriction is that a \neq 0.
LearninDaMath said:
And if b = 0 so that y = ax^2, is it still given the title of quadratic equation?

I would guess yes since it still has a power of 2 and is a parabola. Is this correct?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

High School Strange quadratic manipulation
  • · Replies 6 ·
Replies
6
Views
2K
High School Complete the square, yes, but what does it mean?
  • · Replies 19 ·
Replies
19
Views
3K
MHB [ASK] Proof of Some Quadratic Functions
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Quadratic, cubic, quartic, quintic equations
  • · Replies 16 ·
Replies
16
Views
5K
MHB Determining c in Quadratic Function Turning Point
  • · Replies 6 ·
Replies
6
Views
2K
High School Quadratic with simple meaningful intuitive constants
  • · Replies 2 ·
Replies
2
Views
2K
MHB How Can You Verify the Sum of Roots in a Quadratic Equation?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Can this particular method solve these quadratic equations?
  • · Replies 11 ·
Replies
11
Views
1K
Undergrad Quadratic equation of two variables
  • · Replies 11 ·
Replies
11
Views
2K
MHB How Do A and B as Roots Verify the Properties of a Quadratic Equation?
  • · Replies 11 ·
Replies
11
Views
3K