A quadratic function has one root at 5 and has a vertex point at (7, 2). What is the value of “a”?

where a-term determines the shape of graph.

h-term determines the change of graph for x-axis.

k-term determines the change of graph for y-axis.

Vertex of the graph is at (h,k).

We need to find the value of a-term. We have the given root which we can substitute in the equation.

Also the roots are on x-axis, meaning that the y-value for roots must be 0.

Therefore the value of a is - 1/2. Rewrite the equation as we get the answer.

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950

trapezoid

step-by-step explanation:

first i plotted all my points on a grid graph

i made sure all of them were in the correct quadrant

then i saw it was a trapezoid or a quadrilateral