Question

graph the function to find the zeros. rewrite the function with the polynomial in factored form
$y = 2x^2 + 5x - 7$

the zeros of the function are \boxed{}.
(use a comma to separate answers.)

Explanation:

Step1: Factor the quadratic

We factor $2x^2 + 5x -7$ by finding two numbers that multiply to $2\times(-7)=-14$ and add to 5. These numbers are 7 and -2. Split the middle term and factor:

$$\begin{align*} 2x^2 + 7x -2x -7 &= x(2x+7) -1(2x+7)\\ &=(2x+7)(x-1) \end{align*}$$

Step2: Set factored form to 0

To find zeros, set $y=0$:
$$(2x+7)(x-1)=0$$

Step3: Solve for x

Use zero product property:
For $2x+7=0$: $2x=-7 \implies x=-\frac{7}{2}$
For $x-1=0$: $x=1$

Answer:

$-\frac{7}{2}, 1$