Question

Where do I find the “solution” do a quadratic equation on a graph? How many possible real solutions are there when you solve a quadratic equation?

Answer 1

Q1. The solution for the quadratic equation on a graph is same as the value of x-intercept(zeros)

Q2. discriminant(b^2-4ac) when y=ax^2 + bx + c

there are 3 situations:

1. discriminant > 0 → 2 real solutions(2 x-intercepts/zeros)

2. discriminant = 0 → 1 real solution(1 x-intercept/zero)

3. discriminant < 0 → 0 real solution(0 x-intercept/zero) → also 2 imaginary solution

Hope it helped!

Explanation:

Answer 2

1) You find the solution by identifying the x-intercepts.

2) Possible real solutions:

- One real solution.

- Two distinct real solutions.

Explanation:

1) The graph of a quadratic equation is a parabola.

By definition, the x-intercepts (Where
`y=0`) are the solutions of the quadratic equation .

2) Given a quadratic equation
`ax^2+bx+c=0`, you can know the number of real solutions by using this formula to find the Discriminant :

`D=b^2-4ac`

If
`D=0`, then there is one real solution with multiplicity two.

If
`D>0`, then there are two distinct real solutions.

On a graph:

-If the graph has two x-intercepts, then the quadratic equation has two real solutions.

-If the graph has one x-intercept , then the quadratic equation has one real solution.