What is the maximum number of x-intercepts of any quadratic function?
a. 2
b. 3
c. 1
d. 0

A

Step-by-step explanation:

Quadratic function has a degree of 2, that means the highest power of x is 2.

They have a shape "U" and are known as "parabolas".

They can have 0, 1, or 2 x-intercepts depending on the type of roots (solutions) the equation has.

Imagine a U shaped curve (quadratic) that doesn't intersect x-axis at all. It will have no real solutions.

Now, imagine a U shaped curve (quadratic) that touches the x-axis and goes up or down. That one has two same real solutions.

Third, imagine a U shaped curve (quadratic) that intersects the x-axis TWICE and goes up or down. That one has 2 distinct real solutions.

Hence, the maximum number of x-intercepts any quadratic function can have is "2".

Correct answer is A

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

both triangles are similar because 2 is just smaller than the big one 1 is similar because they are facing different way's but are similar to each other

step-by-step explanation: