In case of a quadratic function, why are there two x-intercepts and one y-intercept?

Answer 1

the quadratic function forms a curve like a U in the cartesian graph or an upside down U. It's bound to pass the x-axis twice and the y axis only once.

Answer 2

By quadratic function,I assume, you are referring to the variable y expressed as a quadratic function of x in the following form

y = ax^2 + bx + c


Now ,if we plot the graph of this function,why do we have only one y-intercept but 2 x-intercepts? Good question.

The y-intercepts of a curve correspond to all those points that have the x-coordinate zero. In other words any curve would intersect the y-axis at ( 0, b) where b is some real number.

In this case, we have y = ax^2 + bx + c. So if we plug x = 0, into the equation ,we get y = c which has only ONE solution in y viz y =c as it's a linear polynomial equation.

On the contrary, the x-intercepts will correspond to all those points that have y = 0. In the above equation, this would lead to ax^2 + bx + c = 0.This equation, as you should be knowing,has two roots ,in general, unless b^2 - 4ac = 0,in which case,there will be exactly one root.

This explains why , in general, we would have two x-intercepts and one y-intercept in case of a quadratic function.

Answer 3

2 x intercepts is some of the time. Quadratic equations graph to be parabola's. Looks like a big U.

y = x^2

x = 0 y =0 , x = 1, y=1, x= -1 y= 1 , x= 2 y = 4, x= -2, y+4

Answer 4

Because, in the form of the quadratic function the x is to the power of 2 (x^2) and the y is to the power of one (just y). The power of the variable also tells you how many solutions there are... so since the x is to the power of two it has 2 solutions (and can have 2 x-intercepts). The y is to the power of one, there for it can only have one value.

Answer 5

Consider the quadratic eqn
y = ax^2 + bx + c
For every value of x, there is a single value of y. But the square on the x drives the eqn to be bumpy, and, may, but not necessarily cross the x-axis.

Answer 6

2. because of the fact the x term is on the left of the = sign. the y term is to the main suitable of the = sign and this is concept to be 0. additionally, whilst a detrimental quantity is squared, this is going to become helpful. So x ought to = +4 or -4. Squaring the two one leads to +sixteen. to alter it to 2 y-intercepts and one x-intercept, the x term could could desire to = 0 on the main suitable component and the y words could be to the left of the = sign. 3 & 4 are on your math e book. 5. with out algebra, shall we not remedy any problems previous addition and subtraction. very few issues are geared up with out algebra being in touch in some vogue. It become with algebra (and trigonometry) that the Egyptians have been waiting to construct the pyramids to the precision that they are. Eratosthenes could not ascertain the dimensions of the earth. The checklist could be longer that Y!A ought to enable.