Answer:
VERTEX: (8,1)
GRAPH BY DESMOS IS ATTACHED TO THIS POST
Y-INTERCEPT: (5,0)
X-INTERCEPT: NONE
Explanation:
To find the vertex, we usually use the formula -b/2a to find the x-vertex. So, the x-vertex would be:
-(-4)/2
4/2
2
The y-vertex can be found by substituting the x-vertex back into the equation. So:
y=(2)² -4(2) + 5
y= 4-8+5
y= -4 + 5
y= 1
So, we found that our vertex is (8,1)
Because we see that our "a" value from our quadratic equation is positive, this tells us that the graph opens upwards. We know our vertex is higher than our x-axis line, so there will be no x-intercepts.
The y-intercept is found when the x-value equals to 0. So, inserting this into the equation, we get :
y=(0)² - 0 +5
y= 5
So, we have found our y-intercept as (0, 5)
The graph you could've made would've been using the vertex and the y-intercept and connecting those points for one side of the quadratic graph. The other side would require an integer point for more accuracies, and I believe that the point (3,2) also works.
So, using the points (3,2), (0,5), and (8,1), we can make a graph!
I hope this helped :P