what are the x-intercepts here?
y=x^2+2x-35
y=x^2+2x-48
I will do one: X intercept is when y is zero.
0=x^2+2x-35
0=(x+7)(x-5)
x=5,x=-7
To find the x-intercepts of a quadratic equation, we need to set y equal to zero and solve for x.
For y = x^2 + 2x - 35:
Step 1: Set y equal to zero: 0 = x^2 + 2x - 35
Step 2: Factor the quadratic equation: 0 = (x - 5)(x + 7)
Step 3: Set each factor equal to zero and solve for x:
x - 5 = 0 or x + 7 = 0
x = 5 or x = -7
Therefore, the x-intercepts for y = x^2 + 2x - 35 are x = 5 and x = -7.
For y = x^2 + 2x - 48:
Step 1: Set y equal to zero: 0 = x^2 + 2x - 48
Step 2: Factor the quadratic equation: 0 = (x - 6)(x + 8)
Step 3: Set each factor equal to zero and solve for x:
x - 6 = 0 or x + 8 = 0
x = 6 or x = -8
Therefore, the x-intercepts for y = x^2 + 2x - 48 are x = 6 and x = -8.
To find the x-intercepts of a quadratic equation, you need to set the equation equal to zero and solve for x. The x-intercepts are the points where the graph of the equation crosses the x-axis.
For the first equation, y = x^2 + 2x - 35, set y equal to zero:
0 = x^2 + 2x - 35
To solve for x, you can either factor the equation or use the quadratic formula. Let's use factoring in this case.
Since the coefficient of x^2 is 1, look for two numbers that multiply together to give you -35 (the coefficient of the constant term) and add up to give you 2 (the coefficient of x). The numbers are 7 and -5.
So the factored form of the equation is:
0 = (x + 7)(x - 5)
Now, set each factor equal to zero and solve for x:
x + 7 = 0
x = -7
x - 5 = 0
x = 5
Therefore, the x-intercepts for the first equation are x = -7 and x = 5.
Now let's move on to the second equation, y = x^2 + 2x - 48.
Again, set y equal to zero:
0 = x^2 + 2x - 48
To solve for x, use either factoring or the quadratic formula. Let's use factoring.
Look for two numbers that multiply together to give you -48 and add up to give you 2. The numbers are 8 and -6.
The factored form of the equation is:
0 = (x + 8)(x - 6)
Now, set each factor equal to zero and solve for x:
x + 8 = 0
x = -8
x - 6 = 0
x = 6
Therefore, the x-intercepts for the second equation are x = -8 and x = 6.
To summarize:
For the first equation, y = x^2 + 2x - 35, the x-intercepts are x = -7 and x = 5.
For the second equation, y = x^2 + 2x - 48, the x-intercepts are x = -8 and x = 6.