The problem has two parts. First, we need to find the points of intersection of two given graphs, $y = 2x + 5$ and $y = 2x^2 + x - 1$. Second, we need to find the value of $y$ on the curve $y = 2x^2 + x - 1$ when $x = -2.5$.

1. Problem Description

The problem has two parts.

First, we need to find the points of intersection of two given graphs, $y = 2x + 5$ and $y = 2x^2 + x - 1$.

Second, we need to find the value of $y$ on the curve $y = 2x^2 + x - 1$ when $x = -2.5$.

2. Solution Steps

Part 1:

To find the points of intersection, we need to solve the system of equations:

$y = 2x + 5$

$y = 2x^2 + x - 1$

Set the expressions for $y$ equal to each other:

$2x + 5 = 2x^2 + x - 1$

Rearrange the equation to form a quadratic equation:

$2x^2 + x - 1 - 2x - 5 = 0$

$2x^2 - x - 6 = 0$

We can factor this quadratic equation:

$(2x + 3)(x - 2) = 0$

So, the solutions for $x$ are:

$2x + 3 = 0 \Rightarrow x = -\frac{3}{2} = -1.5$

$x - 2 = 0 \Rightarrow x = 2$

Now, we find the corresponding $y$ values:

For $x = -1.5$, $y = 2(-1.5) + 5 = -3 + 5 = 2$

For $x = 2$, $y = 2(2) + 5 = 4 + 5 = 9$

Therefore, the points of intersection are $(-1.5, 2)$ and $(2, 9)$.

Part 2:

We are given $x = -2.5$ and the curve $y = 2x^2 + x - 1$.

Substitute $x = -2.5$ into the equation:

$y = 2(-2.5)^2 + (-2.5) - 1$

$y = 2(6.25) - 2.5 - 1$

$y = 12.5 - 2.5 - 1$

$y = 10 - 1$

$y = 9$

Thus, the value of $y$ on the curve when $x = -2.5$ is $9$.

3. Final Answer

For Question 48, the points of intersection are (2.0, 9.0) and (-1.5, 2.0).

For Question 49, if $x = -2.5$, the value of y on the curve is

9. The answer for Question 48 is A.

The answer for Question 49 is C.