# Graph of the Function

• Nov 16th 2008, 09:47 PM
magentarita
Graph of the Function
If the roots of
ax^2 + bx + c = 0 are real, rational, and equal, what is true about the graph of the function
y = ax^2 + bx + c?

(1) It intersects the
x-axis in two distinct points.
(2) It lies entirely below the
x-axis.
(3) It lies entirely above the
x-axis.

(4) It is tangent to the
x-axis.
• Nov 17th 2008, 12:15 PM
masters
Quote:

Originally Posted by magentarita
If the roots of

ax^2 + bx + c = 0 are real, rational, and equal, what is true about the graph of the function

y = ax^2 + bx + c?

(1) It intersects the x-axis in two distinct points.
(2) It lies entirely below the x-axis.
(3) It lies entirely above the x-axis.
(4) It is tangent to the x-axis.

The answer is (4) It is tangent to the x-axis.

If the roots are equal, then it is called a 'double root', thus touching the x-axis at only one point, the point of tangency to the x-axis (also the vertex of the parabola). A double root also refers to a zero of a polynomial function with multiplicity 2.

Example: \$\displaystyle y=x^2+4x+4\$

\$\displaystyle x^2+4x+4=0\$

\$\displaystyle (x+2)(x+2)=0\$

\$\displaystyle x=2 \ \ or \ \ x=2\$

• Nov 17th 2008, 10:11 PM
magentarita
tell me.........
Quote:

Originally Posted by masters
The answer is (4) It is tangent to the x-axis.

If the roots are equal, then it is called a 'double root', thus touching the x-axis at only one point, the point of tangency to the x-axis (also the vertex of the parabola). A double root also refers to a zero of a polynomial function with multiplicity 2.

Example: \$\displaystyle y=x^2+4x+4\$

\$\displaystyle x^2+4x+4=0\$

\$\displaystyle (x+2)(x+2)=0\$

\$\displaystyle x=2 \ \ or \ \ x=2\$

Tell me, where do you find the answers? How do you know so much about math? Do you search online for the answers or your math books?