Graph the parabola, \[ y=2 x^{2}+8 x+4 \] Plot five points on the parabolas the vertex, twe points to the left of the vertex, and two points to the right of the vert button.

We want to graph the parabola given by   y = 2x² + 8x + 4. Step 1. Find the vertex. The x-coordinate of the vertex for a parabola in the form y = ax² + bx + c is given by x = –b⁄(2a). Here, a = 2 and b = 8, so   x = –8⁄(2×2) = –8⁄4 = –2. Now substitute x = –2 into the equation to find y:   y = 2(–2)² + 8(–2) + 4    = 2(4) – 16 + 4    = 8 – 16 + 4    = –4. So the vertex is (–2, –4). Step 2. Choose two points to the left of the vertex. It’s usually useful to pick x-values less than –2. • Let x = –3:   y = 2(–3)² + 8(–3) + 4    = 2(9) – 24 + 4    = 18 – 24 + 4    = –2.   So one point is (–3, –2). • Let x = –4:   y = 2(–4)² + 8(–4) + 4    = 2(16) – 32 + 4    = 32 – 32 + 4    = 4.   So another point is (–4, 4). Step 3. Choose two points to the right of the vertex. Pick x-values greater than –2. • Let x = –1:   y = 2(–1)² + 8(–1) + 4    = 2(1) – 8 + 4    = 2 – 8 + 4    = –2.   So one point is (–1, –2). • Let x = 0:   y = 2(0)² + 8(0) + 4    = 0 + 0 + 4    = 4.   So the other point is (0, 4). Step 4. List the five points:  • Vertex: (–2, –4)  • Left of vertex: (–3, –2) and (–4, 4)  • Right of vertex: (–1, –2) and (0, 4) Step 5. Graphing the Parabola. 1. Plot the vertex at (–2, –4). 2. Plot the two points to the left: (–3, –2) and (–4, 4). 3. Plot the two points to the right: (–1, –2) and (0, 4). 4. Draw a smooth curve through these points. Notice that the parabola is symmetric with respect to the vertical line x = –2. A rough sketch would look like this:          (–4,4)         (0,4)               /    \          (–3,–2)    (–1,–2)               |                   (–2,–4) Since the coefficient of x² is positive (a = 2 > 0), the parabola opens upward. With these points and steps, you now have a clear plot of the parabola y = 2x² + 8x + 4.