Solve for xxx. write the smaller solution first, and the larger solution second. x^2 + 3x - 10 = 0x 2 +3x−10=0x, start superscript, 2, end superscript, plus, 3, x, minus, 10, equals, 0 \text{smaller }x = smaller x=s, m, a, l, l, e, r, space, x, equals \text{larger } x = larger x=l, a, r, g, e, r, space, x, equals

Step-by-step explanation:

We have been given an equation . We are asked to find the solutions of our given equation.

We will use splitting the middle term method to solve quadratic equation.

We will split middle term of our given equation into parts such that whose product is and whose sum is 3.

We know that such two numbers are .

Using zero product property, we will get:

Therefore, the solutions for our given equation are .

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1