# What are the points of intersection of y=-2x^2-5x+3 and y=-2x+3?

Sep 5, 2016

$\left(0 , 3\right) , \mathmr{and} , \left(- \frac{3}{2} , 6\right)$.

#### Explanation:

To find the pts. of intersection of these two curves, we have to solve

their eqns.

$y = - 2 {x}^{2} - 5 x + 3 , \mathmr{and} , y = - 2 x + 3$

$\therefore - 2 x + 3 = - 2 {x}^{2} - 5 x + 3 , \mathmr{and} , 2 {x}^{2} + 3 x = 0$

$\therefore x \left(2 x + 3\right) = 0$

$\therefore x = 0 , x = - \frac{3}{2}$

$\therefore y = - 2 x + 3 = 3 , y = 6$

These roots satisfy the given eqns.

Hence, the desired pts. of int. are $\left(0 , 3\right) , \mathmr{and} , \left(- \frac{3}{2} , 6\right)$.

Sep 5, 2016

At points (0, 3); (-1.5, 6)  the two curves intersets

#### Explanation:

Given -

$y = - 2 {x}^{2} - 5 x + 3$
$y = - 2 x + 3$

To find the intersection point of these two curves, set -

$- 2 {x}^{2} - 5 x + 3 = - 2 x + 3$

Solve it for $x$

You will get at what values of $x$ these two intersect

$- 2 {x}^{2} - 5 x + 3 + 2 x - 3 = 0$
$- 2 {x}^{2} - 3 x = 0$
$x \left(- 2 x - 3\right) = 0$
$x = 0$
$x = \frac{3}{- 2} = - 1.5$

When $x$takes the values 0 and - 1.5 the two intersects

To find the point of intersection, we must know the Y-cordinate

Substitute $x$ in any one of the equations.

$y = - 2 \left(0\right) + 3$
$y = 3$

At $\left(0 , 3\right)$ the two curves intersets

$y = - 2 \left(1.5\right) + 3 = 3 + 3 = 6$

At $\left(- 1.5 , 6\right)$ the two curves intersects