George Bush faces his final and biggest test of the Republican National Convention Thursday night when he gives his acceptance speech - and tries to live up to the tough-leader image painted by speakers all week.

He will be under pressure to match the emotion of Ronald Reagan's speech Monday night - and, of course, Michael Dukakis' eloquent speech before Democrats in Atlanta last month. A great speech might help Bush finally catch Dukakis in the polls, and a bad one could make him lose ground.Bush's chosen running mate, Sen. Dan Quayle, R-Ind., will also give Americans their first close look at him as he gives his acceptance speech during prime time.

Winning the Republican nomination Wednesday night was easy for Bush - it came on the first ballot when Texas put him over the top as Bush's son George Jr. announced the vote. Bush has had enough delegates to win the nomination since the Utah caucuses put him over the top on April 25.

After a long celebration - and after most networks signed off for the night - the Utah delegation cast its 26 votes for Bush.

Gov. Norm Bangerter announced the vote saying, "Utah, a great and pretty state, a state of industry, a state of education, a state of opportunity, a state with the greatest snow on earth and the greatest earth on snow, the home of the great Senators Hatch and Garn and Congressmen Nielson and Hansen and soon-to-be Congressman Snelgrove, the state that gave the Reagan-Bush ticket the highest percentage in 1980 and 1984 and will do the same for the Bush-Quayle ticket, is proud to cast our 26 votes for the next president of the United States of America, George Bush."

Speakers used all of prime time at the convention on Wednesday to paint Bush as a tough, competent leader who is strong on education, the family and holding the line on taxes. They also said he would save America from the sure disaster they say Michael Dukakis would bring.

Former presidential candidate Sen. Bob Dole said Dukakis is "one of those liberals with strange ideas - Dukak-eyed ideas - about the way the world works," but that Bush understands it well.

He asked if Democrats had been elected in 1984, "Would there have been an improvement in relations with Moscow and an INF treaty?" The audience yelled, "No!" Dole said, "You're right - and I'll tell you why: because these liberals define arms control this way: the Soviets arm while we control."

He added, "George Bush and Dan Quayle support freedom fighters around the world. And what does the Democratic candidate support? What programs to keep America truly strong and free? Let me list of of them for you." Silence followed. "I haven't lost my place, I just can't think of any."

Sen. Pete Domenici, R-N.M., who was once considered a finalist as Bush's running mate, said Bush has proved can make tough decisions such as when he and President Reagan cut taxes and held down federal spending to reduce inflation and create jobs.

"That was tough medicine, but it worked," he said, adding that Dukakis has ignored such accomplishments.

"The Democratic candidate has adopted what I call an ostrich strategy: bury his head in the sand and pretend American men and women aren't working, pretend the American industry is not producing, and try to make the American people fear a future they need not fear. Let him leave his head in the sand - 117 million American working men and women know better."

Texas Sen. Phil Gramm, who was a Democrat and is now a Republican, in nominating Bush depicted the vice president as courageous and tough, telling how in World War II Bush's bomber was hit and both his crewmen were killed.

"As flames swept over the wings and cockpit, George Bush remembered the first obligation of a leader is to accomplish the mission. He stayed on his bombing run and dropped two tons of TNT on the target. He then turned his crippled plane out to sea and bailed out.

"The Japanese sent boats to capture him, but his fellow pilots hovered over him, strafing the Japanese to keep them back. With blood streaming down his face and a .38 revolver in one hand, he paddled away from the shore with the other hand to be rescued by a submarine."

Gramm concluded saying, "I am honored to place in nomination the name of a man who has served America in war and in peace, who has the experience, the character and the strength to lead this great land we love." The crowd went wild in celebration for more than 15 minutes, screaming, waving flags and stomping on balloons.

Pennsylvania State University football coach Joe Pa-terno gave a seconding speech for Bush's nomination, saying, "I know a leader and I know a winner. I know the difference between bravado and the quiet, dignified, confidence of a Joe DiMaggio, a Walter Payton . . . a George Bush."

But Paterno said, "I'm here because I believe in quality education on all levels. George Bush will be an education president."

Agreeing with that assessment was Education Secretary William J. Bennett. "George Bush knows about the importance of standards, discipline, choice, accountability and the teaching of right and wrong. George Bush has the experience and the guts to lead this country . . . He will educate our precious children."

U.S. Labor Secretary Ann McLaughlin also said Bush is a friend of the working man, and to this day carries a membership card from the United Steelworkers of America.

"That Steelworkers union card dates from his early days in Texas when he worked in the oil field right after the war. He rolled up his sleeves, got his hands dirty, started a business, created jobs and met a payroll."

In Utah, Sen. Jake Garn, R-Utah, also hailed the selection of Quayle.

"I think he will add a great deal to the presidential ticket of George Bush. He is a man of strong conservative ideals and is particularly strong in the area of national defense - an area in which Michael Dukakis is weak," Garn said.

He will also be helpful with the younger voters. While he is somewhat unknown nationally, once the public becomes familiar with him and his experience and qualifications, the fact that he is relatively unknown will not be a problem.