How many solutions does the quadratic y=x2+4x−5

Question

𝑦
=
𝑥
2
+
4
𝑥
−
5
have?

Reference Sheet - Number of Quadratic Solutions

(1 point)
Responses

No real number solutions
No real number solutions

Two real number solutions
Two real number solutions

One real number solution
One real number solution

Answer 1

To determine the number of solutions for the quadratic equation \( y = x^2 + 4x - 5 \), we can analyze it using the discriminant.

The general form of a quadratic equation is \( ax^2 + bx + c = 0 \), where:

• \( a = 1 \)
• \( b = 4 \)
• \( c = -5 \)

The discriminant \( D \) is calculated using the formula: \[ D = b^2 - 4ac \]

Substituting in our values: \[ D = (4)^2 - 4(1)(-5) \] \[ D = 16 + 20 \] \[ D = 36 \]

Since the discriminant \( D \) is positive (specifically, \( D = 36 \)), it indicates that there are two real number solutions for the quadratic equation.

Thus, the correct response is: Two real number solutions.